
v-^ET 



Hydromechanics 
Mine Drainage 




I.C.S. STAFF 



HYDROMECHANICS 
MINE DRAINAGE 



449 

Published by 

INTERNATIONAL TEXTBOOK COMPANY 

SCRANTON, PA. 



^D-MqD-T* 






Hydromechanics: Copyright, 1906, by International Textbook Company. 
Mine Drainage: Copyright, 1906, by International Textbook Company. 



Entered at Stationers' Hall, London 



All rights reserved 



Printed in U. S. A. 









International Textbook Preso 
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CONTENTS 

Note. — This book is made up of separate parts, or sections, as indicated by 
Jr their titles, and the page numbers of each usually begin with 1. In this list of 
-1 contents the titles of the parts are given in the order in which they appear in 
1 the book, and under each title is a full synopsis of the subjects treated. 



HYDROMECHANICS 

Pages 
Hydrostatics 1-1 1 

Laws of liquid pressure; Pascal's law; Downward, up- 
ward, and lateral pressures; Hydraulic jack; Buoyant 
effects of water. 

Hydraulics 12-45 

Definitions and Explanations 12-19 

Mean velocity; Velocity of efflux; Equivalent head ; Con- 
tracted vein. 

Flow of Water Through Pipes 20-35 

Hydraulic Grade Line 20-22 

Flow of Water Through Long Pipes 23-31 

Darcy's formula; Fundamental formula; Formulas for 
smooth pipes ; Formulas for velocity. 

Flow of Water Through Short Pipes 32-33 

Other Losses of Head 34-35 

Flow of Water Through Open Channels. 36-38 

Weirs 39-45 

Forms of weir; Crest of weir; Discharge of weir. 



CONTENTS 



MINE DRAINAGE 

Pages 

Surface Drainage 1-3 

Keeping surface water from the mine ; Flow of water 
into the mine ; Variation in amount of water. 

Underground Drainage 4—21 

Drainage of Flat Deposits Above Water Level 4-7 

Adit drainage ; Swamp drainage ; Contour drainage map ; 
Drainage of temporarily abandoned mines and robbed 
areas. 

Flat Deposits Below Water Level 8-11 

Sumps ; Shaft lodgment. 

Inclined Deposits Above Water Level 12-14 

Adit drainage; Drainage tunnels. 

Inclined Deposits Below Water Level 15-16 

Drainage of Working Places 17 

Tapping and Draining Abandoned Workings 18-21 

Draining off water; Tapping a body of water from below; 
Barrier pillars. 

Mine Dams 22-32 

Use and location of dams ; Water pressure on dams ; 
Wedge-shaped wooden dam; Flat wooden dam; Brick 
dams; Stone dams; Shaft dams; Thickness of mine 
dams. 

Siplions 33-38 

Construction; Air in siphon; Discharge of a siphon. 

Water Hoisting 39-53 

Bucket Drainage 39-40 

Water Buckets and Tanks 41-50 

Water-bucket valves ; Automatic bucket dumps ; Water 
tanks ; Water tank car wheels ; Speed of hoisting water 
on slopes ; Operation of tanks ; The Gilberton water 
shaft. 

Cost of Water-Hoisting Plants 51-53 



HYDROMECHANICS 

Serial 853 Edition 1 

HYDROSTATICS 



LAWS OF LIQUID PRESSURE 

1. Hydrostatics treats of the pressure and equilibrium 
of practically incompressible fluids. A pressure of 15 pounds 
per square inch compresses water less than 200V00 of its 
volume; water is, therefore, practically incompressible. 



Fig. 1 represents two cylindrical vessels of the same 
The inside of vessel a is 



2. 

size. 

fitted with a wooden block up to 
the piston P; the vessel b is filled 
with water to a depth equal to 
the length of the wooden block 
in a. Both vessels are fitted 
with air-tight pistons P, whose 
areas are each 10 square inches. 
Suppose, for convenience in 
calculation, that the weights of 
the cylinders, pistons, block, and 
water be neglected, and that a 
force of 100 pounds be applied 
to both pistons. The pressure 
per square inch will be 1 ro~ = 10 
pounds. This pressure will be transmitted to the bottom of 
the vessel a and will be 10 pounds per square inch; there 
will be no pressure on the sides. In the vessel b, the pressure 

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Fig. 1 



2 



HYDROMECHANICS 



on the bottom will be the same as in the other case, that is, 
10 pounds per square inch, but, owing to the fact that the 
molecules of the water are perfectly free to move, this pres- 
sure is transmitted in every direction with the same intensity; 
that is to say, the pressure at any point, c, d, e, f,g, h, etc., 
due to the force of 100 pounds, is exactly the same and 
equals 10 pounds per square inch. 



3. Pascal's Liaw. — The pressure per unit of area exerted 
anywhere on a mass of liquid is tra?ismitted undiminished in all 
directions and acts with the same intensity on all surfaces in a 
directio7i at right angles to those surfaces. 

This may be proved experimentally by means of the appa- 
ratus shown in Fig. 2. Let the area of the pistons a, b, c, d, e, 
and /be 20, 7, 1, 6, 8, and 4 square inches, respectively. 

a If the pressure due to 

the weight of the water be 
neglected and a force of 5 
pounds be applied at c 
(whose area is 1 square 
inch), a pressure of 5 
pounds per square inch 
will be transmitted in all 
directions; in order that 
there shall be no move- 
ment, a force of 6 X 5 = 30 
pounds must be applied at 
d, 40 pounds at e, 20 pounds 
at /, 100 pounds at a, and 
35 pounds at b. 

If a force of 99 pounds 
were applied to a, instead of 100 pounds, the piston a would 
rise and the other pistons, b, c, d s e, and /, would move 
inwards; but if the force applied to a were 100 pounds, they 
would all be in equilibrium. Suppose 101 pounds to be 
applied at a;, the pressure per square inch \ Q - = 5.05 pounds 
would be transmitted in all directions; then, since the pres 
sure due to c is only 5 pounds per square inch, it is evident 




HYDROMECHANICS 




that the piston a would move downwards, and the pistons 
b, c, d, e, and / would be forced outwards. 

The pressure due to the weight of a liquid may be down- 
wards, upwards, or sidewise. 

4. Downward Pressure. — In Fig. 3, the pressure on 
the bottom of the vessel a is equal to the weight of the 
water it contains. If the areas 

of the bottoms of vessels a and b ^ 

and the depth of the liquids con- 
tained in them are the same, the g| 
pressures on the bottoms of the H 
vessels will be the same. Sup- 
pose that the bottoms of the 
vessels are 6 inches square, 
that the part c d, in the vessel b, 
is 2 inches square, and that the 
vessels are filled with water. 
The weight of 1 cubic inch of 

62 5 
water is — — = .03617 pound. FlG . 3 

The number of cubic inches in a will be 6 X 6 X 24 = 864. 
The weight of the water will be 864 X .03617 = 31.25 pounds. 
Hence, the total pressure on the bottom of a will be 31.25 
pounds, or .868 pound per square inch. The pressure in b due 
to the weight contained in the part ^ is 6 X 6 X 10 X .03617 
= 13.02 pounds. The weight of the part contained in cd is 
2X 2 X14X .03617 = 2.0255 pounds, and the weight per 

2 0255 

square inch of area in cd is — = .5064 pound. 

4 
According to Pascal's law, this weight (pressure) is trans- 
mitted equally in all directions; therefore, every square inch 
of the top of the large part of the vessel b will be subjected 
to a pressure of .5064 pound. The area of the part be is 
6 X 6 = 36 square inches, and the total pressure due to the 
weight of the water in the small part will be .5064 X 36 
= 18.23 pounds. Hence, the total pressure on the bottom 
of b will be 13.02 + 18.23 = 31.25 pounds, the same result 
as in the case of the vessel a. 



4 HYDROMECHANICS 

If an additional pressure of 10 pounds per square inch 
were applied to the upper surface of both vessels, the total 
pressure on their bottoms would be 31.25 + (6 X 6 X 10) 
= 31.25 + 360 = 391.25 pounds. 

If this pressure were obtained by means of a weight 
placed on a piston, as shown in Figs. 1 and 2, the weight 
necessary to cause this pressure for the vessel a would be 
6 x 6 X 10 = 360 pounds and for the vessel b, 2 X 2 X 10 
= 40 pounds. 



5. .Law. — The pressure on the bottom of a vessel containing 
a fluid is independent of the shape of the vessel ', and is equal to 
the weight of a prism of the fluid whose base is the same as the 
bottom of the vessel and whose altitude is the distance between 
the bottom and the upper surface of the fluid, plus the pressure 
per unit of area o?i the upper surface of the fluid multiplied 
by the area of the bottom of the vessel. 

Suppose that the vessel b, Fig. 3, were 
inverted, as shown in Fig. 4, the pressure 
on the bottom would still be .868 pound 
per square inch, but it would require a 
weight of 3,490 pounds to be placed on a 
piston at the upper surface to make the 
pressure on the bottom 391.25 pounds, 
instead of a weight of 40 pounds, as in the 
other case. 

Example. — A vessel filled with salt water hav- 

fcis3 ing a specific gravity of 1.03 has a circular bottom 

FlG - 4 13 inches in diameter; the top of the vessel is 

fitted with a piston 3 inches in diameter, on which is laid a weight 

of 75 pounds. What is the total pressure on the bottom if the depth 

of the water is 18 inches? 




Solution. — The weight of 1 cu. in. of the water is 



62.5 X 1.03 
1,728 



= .037254 lb. 13 X 13 X .7854 X 18 X .037254 = 89.01 lb. , or the pressure 

75 



due to the weight of the water. 



= 10.61 lb. per sq. in. 



3 X 3 X .7854 

due to the weight on the piston. 13 X 13 X .7854 X 10.61 = 1,408.29 lb. 
Total pressure is 1,408.29 + 89.01 = 1,497.3 lb. Ans. 



HYDROMECHANICS 



6. Upward Pressure. — In Fig. 5 is represented a 
vessel of exactly the same size as that represented in Fig. 4. 
There is no upward pressure on the surface c due to the 
weight of the water in the large part ed, but there is an 
upward pressure on c due to the weight of the water in 
the small part be. The pressure per square inch due to the 
weight of the water in be was found to be .5064 pound; the 
area of the upper surface c of the large part cd is evidently 
(6 X 6) - (2 X 2) = 36 - 4 = 32 square inches, and the 
total upward pressure due to the weight of the water is 
.5064 X 32 = 16.2 pounds. 

If an additional pressure of 10 pounds per 
square inch were applied to a piston fitting 
the top of the vessel, the total upward pres- 
sure on the surface c would be 16.2 + (32 
X 10) = 336.2 pounds. 

Example. — A horizontal surface 6 inches by 4 
inches is submerged in a vessel of water 26 inches 
below the upper surface; if the pressure on the 
water is 16 pounds per square inch, what is the total 
upward pressure on the horizontal surface? 

Solution.— 4 X 6 X 26 X .03617 = 22.57 lb., the 
upward pressure due to the weight of the water. 
6 X 4 X 16 = 384 lb., the upward pressure due to 
the outside pressure of 16 lb. per sq. in. The total 
upward pressure is 384 + 22.57 = 406.57 lb. Ans. 

7. Lateral Pressure. — Suppose that the top of the 
vessel shown in Fig. 6 is 10 inches square and that the pro* 
jections at a and b are 1 in. X 1 in. and 10 inches long. 

The pressure per square inch on the bottom of the vesse: 
due to the weight of a liquid will be 1 X 1 X 18 X the weight 
of a cubic inch of the liquid. 

The pressure at a depth equal to the distance of the upper 
surface of b will be 1 X 1 X 17 X the weight of a cubic inch 
of the liquid. 

Since both these pressures are transmitted in every direc- 
tion, they are also transmitted sidewise, and the pressure per 
unit of area on the projection b is a mean between the two and 
equals 1 X 1 X 17i X the weight of a cubic inch of the liquid. 




6 



HYDROMECHANICS 




To find the lateral pressure on the projection a, imagine 
that the dotted line c is the bottom of the vessel; then the 
conditions will be the same as in the preceding case, except 
that the depth is not so great. 

The lateral pressure on a is thus seen to be 1 X 1 X Hi 
X the weight of a cubic inch of the liquid. 

Example. — (a) A well 3 

T feet in diameter and 20 feet 

EfiEPIE^^|Ei^| deep is filled with water; 

what is the pressure on a 
strip of the wall 1 inch 
wide, the center of which is 
1 foot from the bottom? (6) 
What is the pressure on the 
bottom? (c) What is the 
upward pressure per square 
inch 2 feet 6 inches from 
the bottom? 

Solution.— {a) 1 X 36 
X 3.1416 = 113.1 sq. in., 
the area of the strip. 
113.1 X19X12X .03617 
= 932.71 lb., the total pressure on the strip. Ans. 
{b) The pressure per 

932 71 
square inch will be "' ^- 

= 8.247 lb., nearly. 
Then, 36 X 36 X .7854 
X 20 X 12 X .03617 = 
8,836 lb., the pressure on 
the bottom. Ans. 

(c) 20 - 2.5 = 17.5. 

1 X 17.5 X 12 X .03617 
= 7.596 lb., the upward 
pressure per square inch 

2 ft. 6 in. from the bot- 
tom. Ans. 



8. A tall vessel a 
having a stop-cock b 
near its base and ar- 
ranged to float on the water, as shown in Fig. 7, illustrates 
the effects of lateral pressure. When this vessel is filled 



Fig. 6 




HYDROMECHANICS 7 

with water, the lateral pressures, at any two points of the 
surface of the vessel opposite to each other are equal. Being 
equal and acting in opposite directions, they balance each 
other, and no motion can result; but if the stop-cock is 
opened, there will be no resistance to that pressure acting 
on the surface equal to the area of the opening, and it will 
cause the water to flow out, while its equal and opposite 
force will cause the vessel to move through the water in a 
direction opposite to that of the spouting water. 

9. The laws of liquid pressure given in the preceding 
articles may be embraced in the following formula: 
P = a (dw +p) 




in which a = area of a submerged surface, in square inches; 
d = distance, in inches, of center of gravity of 

surface from surface of liquid; 
w = weight of a cubic inch of the fluid, in pounds; 
p = pressure on surface of liquid, in pounds per 

square inch; 
P = total pressure on submerged surface, in 

pounds. 

10. Since the pressure on the bottom of a vessel due to 
the weight of the liquid is dependent only on the height of 
the liquid, and not on the shape of the vessel, it follows that 



8 



HYDROMECHANICS 



if a vessel has a number of radiating tubes, as shown in 
Fig. 8, the water in each tube will be on the same level, no 
matter what may be the shape of the tubes. For, if the 
water were higher in one tube than in the others, the down- 
ward pressure on the bottom due to the height of the water 
in this tube would be greater than that due to the height 
of the water in the other tubes. Consequently, the upward 
pressure would also be greater, the equilibrium would be 
destroyed, and the water would flow from this tube into the 
vessel and rise in the other tubes until it was at the same 
level in all, when it would be in equilibrium. This principle 
is expressed in the familiar saying, water seeks its level. 

Example. — The water level in a city reservoir is 150 feet above the 
level of the street; what is the pressure of the water per square inch 
on the hydrant? 

Solution.— 1 X 150 X 12 X .03617 = 65.106 lb. per sq. in. Ans. 

11. In Fig. 9, let the area of the 
piston a be 1 square inch, of b 40 square 
inches. According to Pascal's law, 1 
pound placed on a will balance 40 
pounds placed on b. 

Suppose that a moves downwards 10 
inches; then 10 cubic inches of water 
will be forced into the tube b. This 
will be distributed over the entire area 
of the tube b in the form of a cylinder, 
whose cubical contents must be 10 cubic 
fig. 9 inches, whose base has an area of 40 

square inches, and whose altitude must be ^o = i inch; that 
is, a movement of 10 inches of the piston a will cause a 
movement of \ inch in the piston b. The practical applica- 
tion of this principle is shown in the hydraulic jack. 

12. The Hydraulic Jack.— The hydraulic jack, 

Fig. 10, is hollow and is filled with a mixture of water and 
alcohol to prevent freezing in cold weather. A lever a fits 
loosely in a socket on the end of the shaft b, which is con- 
nected by the crank c and the rod g with the piston d. When 




HYDROMECHANICS 9 

the lever a is pushed down, the valve h is closed by the pres- 
sure of the liquid in the space /while the valve j opens and 
allows the liquid to pass through j into the space k\ as k is 




already filled with liquid, the ram /, which slides within the 
barrel m, is lifted. If the lever a be raised, valve h will be 



10 HYDROMECHANICS 

opened and valve j will be closed by the spring n y thus pre- 
venting the return of water from k to i, but allowing water to 
flow from o into i. By again depressing the piston, the ram 
is again raised slightly. If the area of the ram is ten times 
the area of the piston, each pound of pressure on the piston 
will exert 10 pounds on the ram, and if the length of the 
lever a is ten times the distance from the fulcrum b to the 
piston rod, each pound of pressure on the end of the lever 
will exert 10 pounds pressure on the piston, or 100 pounds 
on the ram. But the movement of the ram will be only to"o 
the movement of the end of the lever. 

The ram / cannot descend unless valves 
h and j are opened to allow the liquid to 
escape from k into i and from i into o. 
The lever a has a projection on the under 
side so that when it is pressed down its full 
distance the piston d is a short distance 
above the stem of the valve /. If, how- 
ever, the lever is inserted in its socket 
with the projection upwards, it can be 
depressed far enough so that piston d 
Fig. n opens valve ;*, as shown in Fig. 10 (b). 

At the same time, the spring p forces the sleeve e down- 
wards and the cotter q on the end of the sleeve working in a 
slot in the piston rod opens the valve h. 

The sleeve is connected to the top of the valve by the 
lowering wire / in such a manner that the cotter will not 
strike the valve h while the jack is raising the load. The 
ram can be stopped instantly by raising the lever. 




BUOYANT EFFECTS OF WATER 

13. In Fig. 11 is shown a 6-inch cube entirely submerged 
in water. The lateral pressures are equal and in opposite 
directions. The upward pressure is 6 X 6 X 21 X .03617; the 
downward pressure is 6 X 6 X 15 X .03617; and the difference 
is 6 X 6 X 6 X .03617, the volume of the cube in cubic inches 
X the weight of 1 cubic inch of water. That is, the upward 



HYDROMECHANICS 



11 



pressure exceeds the downward pressure by the weight of a 
volume of water equal to the volume of the body. 

14. This excess of upward pressure acts against gravity; 
consequently, if a body be immersed in a fluid, it will lose in 
weight and amount equal to the weight of the fluid it displaces. 
This is called the principle of Archimedes, because it 
was first stated by him. 

The principle may be experimentally demonstrated with 
beam scales, as shown in Fig. 12. 

From one scale pan suspend a hollow cylinder of metal / 
and below that a solid 
cylinder a, of the same 
size as the hollow part 
of the upper cylinder. 
Put weights in the other 
scale pan until they ex- 
actly balance the two 
cylinders. If a be im- 
mersed in water, the 
scale pan containing the 
weights will descend, 
showing that a has lost 
some of its weight. 
Now fill / with water, 
and the volume of water 
that can be poured into FlG ' 12 

t will equal that displaced by a. The scale pan that contains 
the weights will gradually rise until t is filled, when the 
scales balance again. 

If the immersed body is lighter than the liquid, the upward 
pressure will cause it to rise and extend partly out of the 
liquid, until the weight of the body and the weight of the 
liquid displaced are equal. If the immersed body is heavier 
than the liquid, the downward pressure plus the weight of 
the body will be greater than the upward pressure, and the 
body will fall until it touches bottom or meets an obstruction. 
If the weights of equal volumes of the liquid and the body 




12 HYDROMECHANICS 

are equal, the body will remain stationary and be in equilib- 
rium in any position or depth beneath the surface of the 
liquid. 

An interesting experiment in confirmation of the forego- 
ing facts may be performed as follows: Place an egg in a 
glass jar filled with fresh water. The mean density of the 
egg being a little greater than that of water, it will fall to 
the bottom of the jar. Now dissolve salt in the water, 
stirring it so as to mix the fresh and salt water. The salt 
water will presently become denser than the egg and the egg 
will rise. Now, if fresh water is poured in until the egg and 
water have the same density, the egg will remain stationary 
in any position that it may be placed below the surface of 
the water. 

HYDRAULICS 

15. Hydraulics treats of water in motion. The velocity 
of the water flowing through a given cross-section of any 
channel or pipe is not the same at all points of the cross- 
section, owing to the friction against the sides. The mean 
velocity is the average velocity for the entire cross-section, 
and, unless otherwise stated, the mean velocity is used in 
hydraulic problems. The mean velocity is equal to the 
total quantity discharged divided by the area of the cross- 
section. 

Let Q = quantity, in cubic feet, that passes any section in 
1 second; 
A — area of section, in square feet; 
v = mean velocity, in feet per second. 
Then, Q = A v (1) 

and v = -2 (2) 

A 

Example 1. — The area of a certain cross-section of a stream is 
27.9 square inches; the velocity of the water through this section is 
51 feet per second. What is the quantity discharged in cubic feet? 

27 9 
Solution.— Applying formula 1, Q = — '-r X 51 = 9.9 cu. ft. per sec. 

Ans. 



HYDROMECHANICS 



13 



Example 2.— In example 1, what would the velocity have been to 
discharge the same quantity had the area of the cross-section been 
36 square inches? 



9 9 9.9 X 144 
Solution.— Applying formula 2, v = -^ = ^ 

per sec. Ans. 



39.6 ft. 



144 



16. Velocity of Efflux.— If a small aperture be made 
in a vessel containing water, the velocity with which the 
water issues from the vessel is the same as if it had fallen 
from the level of the surface to the level of the aperture, all 
resistances being neglected. This velocity is called the 
velocity of efflux. 

The vertical height of the 
level surface of the water above 
the center of the aperture is 
called the head. In Fig. 13, 
a is the head for the aperture 
A; b is the head for the aperture 
B; and c is the head for the 
aperture C. 

Let v = velocity of efflux, in 
feet per second; 
h = head, in feet, at the aperture considered. 
Then, the theoretical velocity of efflux is expressed by the 
formula 

v = ^gh (1) 

Here^- = 32.16; that is, the velocity of efflux is the same 
as if the same weight of water had fallen through a height 
equal to its head. 

Were it not for the resistance of the air, friction, and the 
effect of the falling particles, the issuing water would spout 
to the level of the water in the vessel, that is, to a height 
equal to its head. 

Example 1.— A small orifice is made in a pipe 50 feet below the 
water level; what is the velocity of the issuing water? 




Solution.— Applying formula 1, 
per sec. Ans. 



= V2X 32.16X50 = 56.7 ft. 



14 HYDROMECHANICS 

From the foregoing formula, as in the laws of falling 
bodies, 

h = f (2) 

Here, h is called the head due to the velocity v. Conse- 
quently, if the velocity of efflux is known, the head can be 
found. 

Example 2.— An issuing jet of water has a velocity of 60 feet per 
second; what must be the head to give it this velocity? 

Solution. — Applying formula 2, // = = 55.97 ft. Ans. 

L X oZ.iXi 

17. Suppose that a tall vessel is fitted with a piston and 
has an orifice near the bottom fitted with a stop-cock. If an 
additional pressure be applied to the piston, it is evident 
that the velocity of efflux will be increased. 

Let p be the pressure per unit of area at the level of the 
water, due to the additional pressure on the piston. If the 
unit of area is 1 square inch, the height of a column of 
water that will cause a pressure equal to p will be 

■ * = -£- feet 

.03617 X 12 .434 

If the unit of area is in square feet, the height of a column 
of water will be — ^— feet. Denote this height corresponding 

to the additional pressure by h x . The original head of the 
water in the vessel is h; hence, h 1 + h = the total head, and 
the velocity of efflux, when the cock is opened, will be 
v = a/2^- (/z, + h) 

The total head h x -f- h is called the equivalent head, and 
must in all cases be reduced to feet before substituting in 
the formula. 

Example. — The area of a piston fitting a vessel filled with water is 
27.36 square inches. The total pressure on the piston is 80 pounds, the 
weight of the piston is 25 pounds, and the head of the water at the 
level of the orifice is 6 feet 10 inches; what is the velocity of efflux, 
assuming that there are no resistances? 

Solution. — 80 + 25 = 105 lb., the total pressure on the upper sur- 
face of the liquid. _ 7 = 3.838 lb. per sq. in. 



HYDROMECHANICS 15 

m inches, due to the pressure of 105 lb. — -^ — = 8.84 ft. = h x . 6 ft. 
10 in. = 6.8333 ft. = h. Hence, applying the formula, 
v = <2g (8.84 + 6.8333)" = V2 X 32.16 X 15.6733 = 31.75 ft. per sec. 

Ans. 

18. When water issues from the side of a vessel, it is 
subjected to the same laws that govern projectiles. The 
range may be calculated in the same manner by taking the 
velocity of efflux as the initial velocity of the projectile. 

The range may be calculated more conveniently by the 
formula 

R = V4 hy 
in which R = range; 

h = head or equivalent head at level of orifice; 
y = vertical height of orifice above point where 
water strikes. 
In Fig. 14, the upper surface of the water is free. For the 




orifice E, h = BE and y = E A; foi the orifice C, h — B C 
and y = CA. 

The greatest range is obtained when h = y; that is, when 
the orifice is half way between the upper surface of the water 
and the level of the place where the stream strikes. If two 
orifices are situated equally distant from the middle orificd 



16 



HYDROMECHANICS 



giving the greatest range, as C and E, Fig. 14, the ranges of 
water issuing from them will be equal. 

Example. — The vertical height above the ground of the surface of 
the water in a vessel is 12 feet. If an orifice is situated 4 feet from 
the upper surface, what is the range? Where is the other point of 
equal range? What is the greatest range? 

Solution.— Applying the formula, R = V4 X 4 (12 - 4) = 11.31ft., 
nearly; greatest range = *v/4 X 6 X 6 = 12 ft., and 6 — 4 = 2; hence, the 
point of equal range is 6 + 2 = 8 ft. below the surface of the water. 

Ans. 

Proof.— Range = V4 hy = V4 X 8 X 4 = 11.31 feet, as 
before. 

19. When the water flows through an 
orifice in the bottom of the vessel and the 
orifice is of large size compared with the 
area of the base, a different rule must be 
used from that given above. In Fig. 15, 
suppose that the area of the orifice in the 
bottom of the vessel is a and that the area 
of the bottom is A; then the velocity v is 
expressed by the formula 




Igh 



A' 



If the area of the orifice is not more than one-twentieth of 
the area of the cross-section of the vessel, use formula 1, 
Art. 16. 

Example 1. — A vessel has a rectangular cross-section of 11 in. 
X 14 in.; the upper surface of the water is 14 feet above the bottom. 
If an orifice 4 inches square is made in the bottom of the vessel, what 
will be the velocity of efflux? 

Solution. — Area of the cross-section is 14 X 11 = 154 sq. in. Area 
16 _ _1_ 
154 ~ 9.62 

orifice is greater than one-twentieth the area of the bottom, apply the 
formula, 



of orifice is 4 X 4 = 16 sq. in. 



Since the area of the 



2gh = / 2X 



32.16X14 



16 a 
154 a 



= 30.17 ft. per sec. Ans. 



HYDROMECHANICS 



17 



Example 2.— (a) If the orifice had been 2 inches square in exam- 
ple 1, what would have been the velocity of efflux? (6) If it had been 
8 inches square? 

4 1 

Solution.— (a) 2 X 2 = 4 sq. in., area of the orifice. — = ^-^. 

Since the area of the orifice is less than one-twentieth the area of the 
vessel, apply formula 1, Art. 16, 

v = yl2gJi = V2 X 32.16 X 14 = 30.008 ft. per sec. Ans. 
(A) 8 X 8 = 64 sq. in., the area of the orifice in the second case; 
then, applying the formula in Art. 19, 

27F = )2 X 32.16 X 14 = 3299ftec A ^ 
_a 2 _ I fr^_ 

A 2 \ 154 2 

20. The Contracted Vein. — When water issues from 
an orifice in a thin plate (Fig. 16) or from a square-edged 




orifice (Fig. 17), the stream is contracted a short distance 
from the orifice and expands again to the full size of the 
orifice. The point at which the contraction is greatest is at 
a distance from the orifice equal to the diameter of the orifice. 
In consequence of this contraction, the velocity of efflux is 
slightly reduced from the theoretical value and the quantity 
discharged is greatly reduced. This contraction is called the 
contracted vein, or vena co?itracta, a name given to it by 
Sir Isaac Newton. 

For ordinary purposes, the actual velocity of efflux may 
be taken as 98 per cent, of the theoretical values calculated by 
the preceding rules. 



18 HYDROMECHANICS 

The actual velocity of efflux from a small orifice is expressed 
by the formula 

v = .98 V2^ 

Example. — What is the actual velocity of discharge from a small, 
square-edged orifice in the side of a vessel, if the head is 20 feet? 
Solution. — Applying the formula, 
v = $%<2gh = .98 V2 X 32.16 X 20 = 35.15 ft. per sec. Ans. 

21. The diameter of the contracted vein at its smallest 
section is about .8 of the diameter of the orifice and its area 
is about .8 X .8 = .64 of the area of the orifice. In Art. 15, 
it was stated that the quantity discharged, in cubic feet per 
second, is equal to the area of the section multiplied by the 
mean velocity, or Q — Av. This is the theoretical value; 
the actual value is the area of the contracted vein multiplied 
by the actual velocity of efflux, or Q = MA X .98 v = .627 
A v; that is, the actual discharge is about .627 of the theo- 
retical discharge. This number .627 is called the coeffi- 
cient of efflux. 

The coefficient of efflux varies somewhat according to the 
head and the size and shape of the orifice; but for square- 
edged orifices or for orifices in thin plates, its average value 
may be taken as .615. Hence, 

Rule. — The actual quantity discharged is .615 times the 
theoretical amount, 
or Q = .615 A v 

Example. — The theoretical discharge from a certain vessel is 
12.4 cubic feet per minute; what is the amount actually discharged 
per second? 

Solution.— 12.4 X .615 = 7.626 cu. ft. per min.; ^- = .1271 

60 

cu. ft. per sec. Ans. 

22. If the water discharges through a short tube, whose 
length is from li to 3 times the diameter of the orifice (see 
Fig. 18), the discharge will be increased. From a large 
number of experiments made by different persons, the 
coefficient of efflux for a short tube may be taken as .815; 
that is, the actual discharge may be taken as .815 times 



HYDROMECHANICS 



19 



the theoretical discharge through an orifice of the same 
size. If the inside edges of the tube are well rounded and 
the tube is conical, as shown in Fig. 19, there will be no 
contraction, and the coefficient of discharge may be taken 





ISIlm 

Pig. 18 Fig. 19 

as .97; that is, the actual discharge through a tube of this 
form will be .97 times the theoretical discharge through an 
orifice whose area is the same as the area of the end of 
the tube. 

23. If in a compound mouthpiece or tube, such as is 
shown in Fig. 20, the narrowest part 
a b be taken as the diameter of the 
orifice, the coefficient of discharge 
may be taken as 1.5526; that is, the 
actual discharge through a compound 
mouthpiece of this shape will be 
1.5526 times the theoretical discharge 
through an orifice whose area. is the 
same as the area of the smallest 
section of the mouthpiece. FlG - ^ 

When the upper surface of the water remains at the same 
height above the orifice, there is said to be a constant head. 
The velocity of efflux varies for different points in the orifice; 
it is greater at the bottom of the orifice than at the top, 
since the head is greater at the bottom. The mean velocity 




20 HYDROMECHANICS 

may be obtained by dividing the quantity of water dis- 
charged, in cubic feet per second, by the area of the 
orifice; or 

v = Q (See formula 2, Art. 15) 
A 

24. Let Q = theoretical number of cubic feet discharged 

per second; 

v = mean velocity through orifice, in feet per 

second; 

A = area of orifice, in square feet; 

h = theoretical head necessary to give a mean 

velocity v; 

Q a = actual quantity discharged, in cubic feet 

per second. 

Then, for an orifice in a thin plate or a square-edged 

orifice (the hole itself may be of any shape — triangular, 

square, circular, etc. — but the edges must not be rounded), 

the actual quantity discharged is 

Q a = .615 Q = .615 Av = .615 A<2gh (1) 

For a discharge through a short tube, as shown in Fig. 18, 

Q a = .815 Q = .815 A v = .815 A <2gh (2) 

For a discharge through a mouthpiece, as shown in Fig. 19, 

Q a = .97 Q = .97 Av = .97 A Algh (3) 

For a discharge through the compound mouthpiece, as 

shown in Fig. 20, the area of the orifice being taken as the 

area of the smallest section, 

Q a = 1.5526 Q =1.5526 A v = 1.5526 A <<lgh (4) 

In these four formulas it is assumed that the head 

remains constant. 

FLOW OF WATER THROUGH PIPES 



THE HYDRAULIC GRADE LINE 

25. The hydraulic grade line, or hydraulic gra- 
dient, is the line drawn through a series of points to which 
water will rise in tubes attached to a pipe through which 
water flows. With a smooth pipe of uniform cross-section 



HYDROMECHANICS 



21 



without bends or other obstructions to flow, it is a straight 
line extending from a point slightly below the surface of the 
water in the reservoir to the end of the pipe. 

In Fig. 21 is shown a long horizontal pipe leading from a 
reservoir to a stop-valve 5. When the valve is open so that 
water from the pipe discharges freely into the atmosphere, 
the hydraulic grade line is the line a d fg. The distance of 
the point a below the surface of the water in the reservoir 
represents the head absorbed in overcoming the resistances 
of entrance to the pipe and in producing the velocity with 




which the water flows. In the same way, the difference in 
the height to which the water rises in any two tubes repre- 
sents the head absorbed in overcoming the resistance to flow 
in the pipe between the points at which the tubes are joined. 
The flow of water through the pipe P would be the same, 
except for the difference due to the different lengths of the 
pipe, whether the pipe were horizontal, as shown, or laid along 
the grade line a dig; or, if the reservoir were deepened and 
the pipe laid along the line a' d' /' '. The pressures in the 
pipe, however, would vary greatly with the different posi- 
tions. If it were laid along the line a dig, there would be 
little or no pressure in any part of it, and if it were perforated 



22 



HYDROMECHANICS 



at the top, little or no water would flow from the perforations. 
In the horizontal position, however, and still more in the 
position a! d' P ', there would be pressure at all points, the 
pressure for any point in the pipe being equivalent to 
the head represented by the vertical distance from that 
point to the hydraulic grade line; and if the pipe were per- 
forated anywhere, water would issue from the perforations. 

26. In laying a line of pipe to connect two points having 
different elevations, it is of the utmost importance to ascer- 
tain the position of the hydraulic grade line. Let A and B, 
Fig. 22, represent two reservoirs connected by a pipe line 




of uniform diameter through which the water flows by 
gravity from the upper to the lower level. The hydraulic 
grade line will be the straight line connecting the two reser- 
voirs; in order to cover the most unfavorable conditions, it 
is usually drawn between the two ends of the pipe line, and 
not from surface to surface of the water in the two reservoirs, 
as the level of these surfaces may vary. The slope of the 

H 



grade line will be represented by : 



In order that the dis- 



charge may take place under the full head, the pipe line must 
never rise above the grade line at any point. 

Should the pipe rise above this grade line, as is shown at 5, 

TT 

Fig. 23, the rate of slope is no longer — through the entire 
pipe line, but it is broken into two others at the point b, 
one - flatter and the other — steeper than —. 
were of the same diameter throughout, it would not discharge 



If the pipe 



HYDROMECHANICS 



23 



as much water as if it were kept entirely under the hydraulic 
grade line a c, because its flow would be governed by the 
flatter hydraulic grade line a b. From b to c the water would 
flow without completely filling the pipe. Sometimes, when 
a rocky ridge must be crossed, where it would be very 
difficult and expensive to keep the pipe low enough, two 
diameters are used; the larger one being laid between a 
and b and the smaller between b and c. By properly pro- 
portioning the diameters to the grades, according to the 




rules for the flow of water through pipes, the desired dis- 
charge can be economically secured. 



FLOW OF WATER THROUGH LONG PIPES 

27. When comparing the length of pipe with head or 
pressure, the diameter of the pipe and the nature of its 
interior surface are so much more important than the head 
k, which is the only factor considered in the formula 
v = Algh, that this formula is not used in connection with 
a long pipe. The velocity of flow and consequent volume 
of discharge through pipes of different diameters and 
under different circumstances can be found only by direct 
experiment. ^___ 



DARCY'S FORMULAS 

28. The French engineer Darcy made a series of experi- 
ments with pipes of different diameters, from which he for- 
mulated certain algebraic expressions that have remained 



24 HYDROMECHANICS 

standard. It was found by these experiments that the 
character of the interior surface of the pipe affected, to a 
remarkable degree, the velocity of the water flowing through 
it. The amount of water flowing with a given head through 
a clean, smooth pipe of given diameter and length was sur- 
prisingly diminished when another pipe, exactly similar, 
except having a rough and dirty interior surface, was sub- 
stituted. The degree of reduction in this case was surpri- 
sing because it had been supposed that the small projections 
caused by the roughness of the surface would, at most, only 
affect the flow by diminishing to that extent the inside 
diameter of the pipe. This would be the case if water were 
a perfect fluid, for then some of the particles of water would 
simply level up the irregularities of the surface and the 
other particles would flow freely over them. Water, how- 
ever, is very far removed from a perfect fluid. It possesses 
the property of viscosity to a great degree, and the particles 
of which it is composed, instead of moving freely over one 
another, are held together by molecular attraction, and it 
requires considerable force to tear them apart. For this 
reason, the term "friction" is misapplied when used to 
express the resistance experienced by water in flowing over 
a rough surface. It is really a resistance to shearing that 
takes place. 

29. It has been found, within the extreme limits of 
roughness and smoothness that exist in practice, that if a 
smooth pipe of given diameter discharges a certain quantity 
of water per second, a rough pipe, otherwise similar, will 
require a diameter 15 per cent, greater to discharge the 
same amount in the same time. Thus, if the smooth pipe 
has a diameter of 36 inches, the rough pipe will require one 
of 41.40 inches to have an equal delivery. Did not this fact 
rest on actual experience, it would seem incredible that 
irregularities amounting to only a fraction of 1 per cent, of 
the diameter of a pipe could affect the flow to such an 
extent. It is explainable, however, the moment the great 
viscosity of water is realized. 



HYDROMECHANICS 25 

These facts led Darcy to divide cast-iron water pipes into 
the two classes already mentioned, smooth and rough, the 
formula for the flow through each being modified by an 
appropriate coefficient. The cleanest and best-conditioned 
pipes will not give a greater discharge than that assigned 
to them by the coefficient for smooth pipes, nor will the 
greatest amount of roughness, from the incrustations to 
which pipes are liable in practice, reduce the flow below that 
for rough pipes, although it frequently approaches it closely. 

30. Fundamental Formula. — Darcy's formula for 
long pipes, by which is understood pipes of 1 ,000 diameters 
and over in length, is 

M- 1 (1) 

CLv 
in which D = diameter of pipe, in feet; 
H = total head, in feet; 
Z,* = total length, in feet; 
v ■ = velocity of efflux, in feet per second; 
C = an experimental coefficient. 
From formula 1, 

\DH 



(2) 

Since the quantity Q, in cubic feet per second, is equal to 
the area A of the pipe, in square feet, multiplied by the 
velocity, in feet per second, 

Q-t+M (3) 

Since A = .7854 D\ 

Q = .7854 O'yj^f- (4) 

which may be written 



4 



617 B° H 



CL 



(5) 



_ ^Although L is, properly speaking, the actual length of the pipe, it 
differs in practice so little from its horizontal projection that the latter 
is taken as being, in general, a sufficiently close approximation. 



26 



HYDROMECHANICS 



31. Coefficients. — The important matter now is to 
know the value of C. For this, Darcy gives the following 
table, based on his experiments. 

It will be observed that the coefficient for smooth pipes is 
in all cases half that of rough ones. As all pipes, no matter 
how clean and smooth they may be when first laid, become, 

TABLE I 

TABLE OF COEFFICIENTS 



Diameters in 


Value of C for 


Value of C for 


Inches 


Rough Pipes 


Smooth Pipes 


3 


.00080 


.00040 


4 


.00076 


.00038 


6 


.00072 


.00036 


8 


.00068 


.00034 


10 


.00066 


.00033 


12 


.00066 


.00033 


14 


.00065 


.00033 


16 


.00064 


.00032 


24 


.00064 


.00032 


30 


.00063 


.00032 


36 


.00062 


.00031 


48 


.00062 


.00031 



in course of time, more or less incrusted, it is safer, in 
practice, to always use the coefficient for rough pipes when 
a permanent system is being laid down. 

32. It will be noticed, from Table I, that the coefficients 
for pipes from 8 to 48 inches in diameter do not greatly 
vary; moreover, from formulas 3, 4, or 5, Art. 30, all other 
conditions being equal, the quantity discharged is affected 
by only the square root of the coefficient, so that slight 
differences in its value are insignificant in reference to the 
volume of water discharged. Formula 5, Art. 30, contains 
the factor .617, and if .000617 be taken as an approximate 



HYDROMECHANICS 27 

coefficient for pipes within limits of 8 and 48 inches, the 
formula becomes 



= / .617 & B H 
y \.000617 L 



whence, Q = ^mjZJl (1) 

If, now, for — , or the total head divided by the total length 

of pipe, the head per thousand, or --r^r, be substituted, this 

formula becomes 

Q=4n r l (2) 

which may be generalized thus: 

-£- = 1 (3) 

h D 5 

In this formula, it must be borne in mind that h is the fall 
per thousand. When logarithms are used, formulas 1 and 2 
are readily solved. Otherwise, they may be more con- 
veniently written: 

Q = D'A~D~h (4) 

— ^==1 (5) 

For pipes of smaller diameter, from 3 to 6 inches, .000785 
is assumed as a coefficient. Then, from formula 5, Art. 30, 



Q = 4 



785 X .785 D s H 



.000785 L 



Q* _ 



whence, -^— = .785 (6) 

h D s 

also Q = .89 a//) 7 ! (7) 

That is to say, for these smaller diameters, the delivery 
will be, in round numbers, about 90 per cent, of that given 
by formula 2, Art. 32. 

33. Formulas for Smooth Pipes. — While in practice 
the formulas for rough pipes should always be used, it is 
sometimes useful to know the probable discharge through 
smooth ones. Since the coefficients for the latter are always 



28 HYDROMECHANICS 

one-half of those of the former, for smooth pipes formulas 
2 and 3, Art. 32, may be written, 

Q = V2 D 5 h (1) 

A = 2 (2) 

Also, from formula 1, 

Q = 1.40 Jzrh (3) 

That is to say, in general, the discharge through a smooth 
pipe is 1.40 times that through a rough pipe of the same diam- 
eter; and reciprocally , the discharge through a rough pipe is 
.70 times that through a smooth one of the same diameter. 
These factors represent the practical limits between which 
the extremes of roughness and smoothness can affect the 
flow through long pipes. 

34. Formulas for Velocity. — Formulas for velocity 
may be derived from those already established. 

Since velocity is equal to quantity divided by area, there 
is obtained from formula 4, Art. 32, for rough pipes of 
from 8 to 48 inches diameter, 

= D % 4Dh 

V .7854 1) 2 
whence, v = 1.27 ^Dh (1) 

For rough pipes of smaller diameter, 

v = 1.13 Wh (2) 

For smooth pipes of large diameter, 

v = 1.78 V^A (3) 

For smooth pipes of small diameter, 

v = l.wJDh (4) 

The ratio of the velocities will be as the quantities; hence, 
the general rule in Art. 33 holds good for relative velocities 
also. 

The terms rough and smooth here, as elsewhere, signify 
the extremes of both cases. 

Example 1. — A rough pipe 16 inches in diameter and 3,700 feet 
long connects two reservoirs, the difference of elevation between the 



HYDROMECHANICS 29 

two being 187 feet; with what velocity does the water flow through 
the pipe? 

Solution. — Substituting in formula 2, Art. 30, 



-=V^OT>o = 10 - 26{t 'P ersec - Ans - 

Example 2. — What is the velocity through the pipe in example 1 
calculated by formula 1, Art. 34? 



Solution.— v = 1.27V| X50.5 = 10.42 ft. per sec. Ans. 

Note.— In approximate formulas, such as all those that apply to the flow of water 
through pipes necessarily are, the results obtained in examples 1 and 2 are equivalent 
to an agreement, and in practice one might happen to be as nearly right as the other. 
It is obvious that when the character of the pipe may vary as to interior surface so 
widely, a very close result can never be hoped for, and all that can be done is to keep 
within probable limits. 

Example 3. — A rough iron pipe 10 inches in diameter is laid with 
a fall of 7i feet per 1,000 feet; what is the discharge? 

Solution. — According to formula 2, Art. 32, Q = AD B h. Sub- 
stituting the values in the above example, (ft) 5 for D 5 and 1\ for h, the 

^~jjn X 7|. Performing the indicated opera- 



tions, \^~n~^jnp~ ~ >/37(Jl = 1.736, which is the discharge in cubic 

feet per second. Ans. 

Example 4. — It is desired to discharge 3 cubic feet per second from 
a pipe line having a fall of 5 feet per 1,000 feet; what diameter of 
rough cast-iron pipe will be required? 

Solution. — Insert the data given in formula 3, Art. 32. Then, 
D = ^f = <IT8 = 1.125 ft., or 131 in., diameter. Ans. 

As cast-iron pipes are made only in full inch sizes, the nearest 
approach to the size would be a pipe 14 in. in diameter. It is usual 
for hydraulic engineers to provide themselves with tables, for the 
purpose of working such intricate examples as occur in this subject. 
Some, however, extract the roots by logarithms. Others provide 
themselves with tables containing fifth roots and their corresponding 
numbers. The extraction of the fifth root of numbers is very long 
and tedious, and the student is referred to the Arithmetic for the 
method of solving such examples. 

Example 5. — It is desired to discharge \ cubic foot per second from 
a 4-inch pipe; what head per 1,000 is necessary to accomplish this? 

Solution.— Substituting the data in formula 6, Art. 32, 

*-™^- 77 - 39 *• Ans - 



30 HYDROMECHANICS 

35, General Relations Between D, Q, L, H, and C, 

and D', Q \ L> ', H' , and C .— From formula 1, Art. 30, we 
have for a given pipe line 

DH 



CLv* 



1 



For any other system, _ , = 1 and — = 1. 

U L' v D' H' C Lv 

C and O will generally be sufficiently near each other to be 

negligible; hence, 

DHL'v'* i 



D'H'Lv* 



(1) 



O* T fi1 7 

Also, from formula 5, Art. 30, there results, ~f 8 = 1 — - 

ni* r r fii7 
and -g^ = ^/. Then, letting C = C, 

~ Q*LD>*H> = (2) 

Q'*L'D*H 
Example. — A pipe 16 inches in diameter, 3,700 feet long, with a 
total fall of 187 feet, has a velocity of 10.26 feet per second; another 
pipe has exactly the same elements, except that its diameter is 18 inches; 
what is its velocity? 

Solution. — Let the elements of the first pipe be D, H, L, and v, 
and those of the second, D', H' , L> ', and v' . By the conditions given, 

Dv'* fjy 

H = H' and L = L' . Then, in formula 1, -r=r. — = = 1, and v' = v\\-fr> 
Substituting the data, 

v' = 10.26 Vpl? = 10.83 ft. per sec. Ans. 

36. From formula 2, Art. 35, Q' = JQ!A D " H ' . If 
L and H equal, respectively, L' and H 1 \ then 

i-S «' 

That is, other elements being equal, the quantities dis- 
charged are as the square roots of the fifth powers of the 
diameters. This is a very important relation. 

Example 1. — A long pipe 24 inches in diameter gives a discharge 
of 2 cubic feet per second; what will be the discharge of a pipe under 
similar circumstances 30 inches in diameter? 



HYDROMECHANICS 31 

Solution. — By multiplying formula 1 by Q and canceling, Q , which 
represents the quantity of water that will be discharged, is obtained 



\W 5 

: follows: Q = Q\~™- B Y substitution, 



Q = ZyJ^Tifiir = 2V(1.25) 5 = 2V3.052 
= 1.747 X 2 = 3.494 cu. ft. discharged per second. Ans. 
Example 2. — A 24-inch pipe discharges 2 cubic feet per second; 
what diameter pipe, with the same length and head, will be required 
in order to discharge 3 cubic feet per second? 

Solution. — The length of the pipe and the head being the same for 

both pipes, they may be neglected and the formula D' = D\\~- may 

be obtained from formula 1, by taking D' s and Z? 5 from under the 
square-root sign and placing Q' 2 and Q 2 under the fifth-root sign. 
Then, by the substitution of the given data in this formula, the diam- 
eter D', which represents the diameter of the pipe sought, may be 
found as follows: 

D> = 2yH = 2 X 1.176 = 2.352 ft. in diameter, or 12" X 2.352' = 28.224 in. 

This would probably be taken in practice as 28 in., for the next 
regular size of cast-iron pipe is 30 in., which is much larger than 
needed. Ans. 

The difference in area between 28-in. and 30-in. diameter pipes is 
91 sq. in., or nearly f sq. ft. The rules given in this Section are only 
approximate, and with pipes from 6 to 24 in. in diameter are liable 
to vary from 5 to 15 per cent. The formulas given are the textbook 
standards, but as stated are not absolutely correct. 

Example 3. — A 24-inch pipe, as in example 1, discharges 2 cubic feet 
per second; how many 8-inch pipes will be required to give the same 
discharge, the heads and lengths being the same? 

Solution. — Let x = the required pipes. Then the number required 
being inversely as the quantity discharged, invert formula 1, and 
obtain 




Inserting the data, x = \Ijt^ = V^J x = V3 3 X 3 2 = 3 V27 = 15.588. 

That is to say, sixteen pipes would be required, each 8 in. in diam- 
eter. Ans. 

The student is again reminded that all the preceding for- 
mulas apply to long pipes only; i. e., those whose length is 
at least 1,000 times the diameter. 



32 



HYDROMECHANICS 



FLOW OF WATER THROUGH SHORT PIPES 

37. All that precedes refers to the flow of water through 
long, rough pipes, where only the head necessary to main- 
tain the flow against the interior resistance of the pipe has 
been taken into account. In such pipes, the additional head 
necessary to overcome resistance to entry into the pipe and 
that necessary to produce the velocity of flow are so insignif- 
icant in comparison with the so-called friction head that they 
are neglected as unnecessarily complicating the formulas. 




In short pipes, however, the case is quite different, and the 
velocity and entrance heads must be taken into account. For 
this purpose, take the entrance head at about one-half the 
velocity head. 

Suppose, for example, that a reservoir, Fig. 24, is tapped 
by a 24-inch pipe 20 feet long, the center of which is 20 feet 
below the surface of the water in the reservoir. What is the 
discharge, using formulas for rough pipe and ignoring the 
modifying action of the reducers shown in the figure? 

What is wanted here is the velocity of efflux, which can be 
obtained in the following manner: 

The total head, 20 feet, is made up of the velocity head, 
the entrance head, and the frictional head. Call the velocity 



HYDROMECHANICS 33 

head x, and the entrance head will then be -. The fric- 

3 x 

tional head call y. Then, — — |- y — 20. The velocity head 
A 

is that required by the law of falling bodies, x = — . The 

velocity and entrance heads together, are, therefore, — . 
From formula 1, Art. 34, g 

v = w^imy 

where h is replaced by its value - L — — . Substituting the 

given data, 

v = 1.27 x kx ll0 ^ y - t and therefore y = z£r. 
\ 20 lol 

From — + y — 20, by substituting — for x, and — — 
L Zg 1 b 1 

for y (neglecting small decimals), v* (tIt + Tgt) = 20. v* 

= ^r X 20 = 678 - 7 ; v = 26 - 05 feet P er second. Area of 
204 

2-foot pipe = 3.1416 square feet. Then the discharge is equal to 

the area of cross-section of the pipe multiplied by the velocity, 

and Q = 26.05 X 3.1416 = 81.84 cubic feet per second. 

38. The formula for finding the diameter of a short 
pipe to convey a given quantity of water with a given head 
is derived from the general formula as follows: 

Solving the form of formula 1, Art. 34, given in the last 

v 2 L 
article for y, y = -z^—z - ; this substituted in the expres- 
1612.9 D 

sion for the total head, 

H = — h y, gives H = h 



4g- ±g 1612.9 D 

Substituting for v its value ^ — , and reducing, 



= 

from which 



H = U + U-±- (1) 

26.45 £> 4 995 £> 5 



D = .251 ^ (37.6 D + L) ( 2 ) 



34 HYDROMECHANICS 

To use this formula, first assume a value for the D under 
the radical sign and solve, thus finding an approximate 
value for D. Then substitute this new value for the D 
under the radical and solve again, and if the new value of D 
agrees closely with the first approximation, the next larger 
commercial size may be taken as the required size of pipe. 
If, however, the second value differs greatly from the first 
approximation, it may be substituted for the D under the 
radical and a new value can thus be found. One or two 
approximations of this kind will usually give a value of D 
that will enable one to select the commercial size nearest to 
the theoretical diameter. 

Example. — What diameter of pipe must be used in order to draw 
17.22 cubic feet of water per second from a reservoir if the total head 
is 20 feet and the pipe is 20 feet long? 

Solution. — Assuming for D a value of 16 in. = 1.33 ft. and 
substituting it for the D under the radical in formula 2, 



D = .251 -\^p (37.6 X 1.33 + 20) = 1.0067 ft., say 1 ft. 
Substituting this value under the radical, 

c /l7 22 2 
D = .251<y^~ (37.6 X 1 + 20) = .968 ft. 

Since this value is so near that of the first approximation, it is plain 
that the required diameter is 1 ft. Ans. 



OTHER LOSSES OF HEAD 

39. Besides the losses of head that have been considered, 
there are minor ones, such as those occasioned by bends, 
changes of grade, or by passing from one diameter to 
another. In general, any such changes in a pipe line pro- 
duces some loss of head, but all such that occur in practice 
are so insignificant in comparison with the loss of head from 
interior surface resistance that no account is taken of them. 
In practice, changes of horizontal direction, when at all pro- 
nounced, are effected by special castings called be?ids, which 
effect the change with very little loss of head; and changes 
of diameter are made through other special castings, called 
reducers, tapering in form, so as to mold the stream of water 



HYDROMECHANICS 



35 



into the proper shape for entering' into the pipe of different 
diameter. Moreover, since water pipes are always cast to 
even sizes, when calculation calls for a fractional diameter, 
as it almost always does, the next larger size of even inches 




is taken, and this is generally more than enough to cover all 
the small losses that can occur from the foregoing causes. 

When bends and elbows are necessary, they should be as 
large as circumstances will per- 
mit, so as to change the direc- 
tion gradually. Sudden changes 
in direction reduce the velocity 
very rapidly, and, consequently, 
reduce the discharge. A reduc- 
tion or increase in the size of 
the pipe, such as connections 
with smaller or larger branch 
pipes, also reduces the velocity 
in the main line. 

Bends should be rounded as shown in Fig. 25, rather than 
sharp, as shown in Fig. 26. A right-angled elbow, as shown 
in Fig. 27, is very destructive to the velocity, and wherever 
a 90-degree turn must be made, a rounded elbow, as in 
Fig. 28, should be used, with the radius made as large as 
possible. 




36 HYDROMECHANICS 

FLOW OF WATER THROUGH OPEN CHANNELS 

40. The amount of water flowing through an open chan- 
nel is found by formula 1, Art 1 5, Q = A v, but the velocity v 
depends on the character of the sides and bottom of the 
channel and the slope is found approximately by the follow- 
ing formulas: 

For channels with earthen banks, 



/lOO, 



000* 



(1) 

For channels lined with dry stone work, 



4 



100,000 s 



(2) 

5r+ 15 

For channels lined with rubble masonry, 



1 100,000, (8) 
\7.3r + 6 



.3r + 6 
For channels lined with wood or brick, 



/ TOO,' 



000* 



(4) 



-+.46 

in which v = mean velocity of flow, in feet per second; 

A 
r = hydraulic radius = — ; 

P 

A = area of water cross-section, in square feet; 

p = wet perimeter, or that portion of outline of cross- 
section of stream in contact with channel, in 
feet; 

TT 

s = slope = ratio — = tangent of slope; 

H = difference in level between ends of channel or 
ditch, or between two points under considera- 
tion; 

L = horizontal length of portion of channel under 
consideration. 

Example. — Referring to Fig. 29 (a) , what is the velocity of flow in 
a timber-lined channel when a b = 26 feet; c d = 16 feet; a c and 



HYDROMECHANICS 



37 



b d = 10 feet each; 
1,000 feet? 
Solution. — 



and e = 9 feet; and the slope equals 1 foot in 



Ass a±+±d xet 



26 + 16 



X 9 = 189 sq. ft. 



= 5.25 



p = ac + cd + db = 10 + 16 + 10 = 36 ft. 

= A = 189 
r ~ p 36 

S = yJ^o = .001 

Substituting these values in formula 4, 



/ 100,000 s _ OK f 



100,000 X .001 



5.251 



V6.6 X5.25 + 
= 8.86 ft. per sec. Ans 

41. If the channel or con- 
duit is entirely enclosed, as 
in Fig - . 29 (b) , and is running 
full of water, but not under 
pressure, the formulas in Art. 
40 apply. If the water is 
under pressure, the formulas 
for pipes must be used. In 
the case of an unlined mine- 
drainage tunnel, it is difficult 
to accurately determine the 
area and wet perimeter owing 
to the irregularity of the rock 
sides and in such a case it is 
best to take average dimen- 
sions for the tunnel and take 
85 to 90 per cent, of the amount of water that would flow 
through a brick-lined tunnel of the same size. 

42. The velocity of flow through a pipe or conduit is 
determined by means of various meters or gauges or by 
direct measurement. The greatest velocity of current occurs 
at a point some distance below the surface in the deepest 
part of the channel. Fairly accurate results may be obtained 
by determining the velocity of the current at various points 
in a carefully surveyed cross-section of the stream. It is 
frequently advantageous to divide the stream into sections 




38 HYDROMECHANICS 

and determine the mean velocity and flow in each section. 
The points for observation should be chosen where the 
channel is comparatively straight and the current uniform. 
Surface floats may be used and the mean velocity of the 
section where the float is used will then be nine-tenths of 
the surface velocity. The total amount of water flowing 
in the stream will be the sum of the amounts in each section. 
The average velocity of the entire stream may be found by 
dividing the total amount of water flowing by the total area 
of the cross-section of the stream. 

43. Size of Channel. — It is often necessary to deter- 
mine the dimensions of a wooden channel or flume to carry 
a given quantity of water. The fol- 
lowing example shows an approxi- 
mate method of doing this: 

Example. — Find the dimensions of a 
wooden flume to carry 250 cubic feet of 
water per second with a grade of 8i feet 
per mile, the width of the flume to be twice 
FlG - 30 the depth of the water flowing through it. 

Solution.— In Fig. 30, if the depth of water in the flume is repre- 
sented by d; the width will be 2d; the wet perimeter^ will be id; the 
area A of the water cross-section will be 2 d X d — 2d 2 ; the hydraulic 

radius r will be - = — = -. The slope 5 is =-^ = .0016; the mean 

. . . 250 250 125 

velocity v is —j- = -— = — - ; substituting these values in formula 



a a 4. a n I 100,000 s 125 d I 

4, Art. 40, v = r^ M ; fM . we have, -^ = - / 



100 ,000 X .00 16 

;xf+.46 



d\ 160 A . 125 d I 160 

= 2\3.3rf+.46' ° r ex P ressed as an equation, -^ = - 2 \j^j^A6> 

squaring both sides of the equation —— — = — r— = — ; d* - 1,289 d 

d 6.6 d -f- .46 

= 179.7. 

Assuming a depth of water of 5 ft. for d and substituting this value 
in the equation 5 6 - 1,289 X 5 = 15,625 - 6,445 = 9,180, which shows 
that the trial value for d is too great. Trying d = 4, 4 6 - 1,289 X 4 
= 4,096 - 5,156 = -1,060, which shows that this value for d is too 
small. Trying d = 4.2 (4.2) 6 - 1,289 X 4.2 = 5,489 - 5,413.8 = 75.2, 
which is less than the required quantity. 



HYDROMECHANICS 



But trying d = 4.3 (4.3) 6 - 1,289 X 4.3 = 6,321.5 - 5,542.7 = 778.8, 
which is too great. Therefore, taking the mean of 4.2 and 4.3 or 4.25 
= 4 ft. 3 in., this value can be verified by calculating the amount of 
water such a flume will discharge under the given conditions, p = 4 d 

36.125 



= 4i X 4 = 17 ft. A = 2d 2 = 2 (4i) 2 = 36.125 sq. ft. r = 



17 



= 2.125. 



■4 



Substituting these values in formula 4, Art. 40, 
= 2.125 



100,000 X s 



4 



100,000 X .0016 



7.06 ft. per sec. 



>r+ .46 " \6.6 X 2.125 + .46 

Hence, Q = A v = 36.125 X 7.06 = 255 cu. ft., which satisfies the con- 
ditions of the problem very closely. Ans. 



WEIRS 

44. A weir is an obstruction placed across a stream for 
the purpose of diverting the water so as to make it flow 
through the desired channel. This channel may be an open- 
ing in the obstruction itself; and it has been found that, when 
properly constructed and carefully managed, such a weir 





forms one of the most convenient and accurate devices for 
measuring the discharge of streams. 

A weir with end contractions is shown in Fig. 31 (a). 
The notch is narrower than the channel through which the 
water ordinarily flows, thus causing a contraction at the 
bottom and two sides of the issuing stream. 



40 HYDROMECHANICS 

A weir without end contractions, also called a weir with 
end contractions suppressed, is shown in Fig. 31 (b) . In this 
case, the notch is the full width of the channel leading to it 
and consequently the stream issuing is contracted at the 
bottom only. 

45. Crest of the Weir. — The edge a, Fig. 31 (c ) and (d) , 
is called the crest of the weir; it should be beveled so that 
the water in passing over it touches only a sharp edge. For 
very accurate work, both side and bottom edges should be 
made from thin plates of metal having a sharp inner edge, 
as shown at <z, Fig. 31 {c); but for ordinary work, the edges 
of the board in which the notch is cut may be beveled, as 
shown in (b) . Frequently, this edge is not made absolutely 
sharp, but is left flat for about i inch, so as to increase the 
strength of the edge and to decrease the liability of its 
being damaged. The bottom edge of the notch must be 
straight and perfectly level; the sides must be at right 
angles to the bottom. The inside edges of the notch must 
always be in a plane at right angles to the surface of still 
water. The head H producing the flow is the vertical dis- 
tance from the crest of the weir to the surface of the water, 
as shown in Fig. 31 (c) and (d)\ this head must be measured 
at a point sufficiently back from the crest so that the surface 
of the water is not affected by the curvature of the stream 
flowing over the weir. 

The distance from the crest of the weir to the bed of the 
stream should be at least three times the head, and with a 
weir having end contractions, the distances from the vertical 
edges to the banks of the stream should each be at least 
three times the head also. The water must approach the 
weir with little or no velocity; to accomplish which it is 
sometimes necessary to provide means, such as baffle boards, 
for reducing the velocity of approach. 



HYDROMECHANICS 41 



DISCHARGE OF WEIRS 

46. When the dimensions of the notch and the head on 
the crest of a weir are known, the discharge can be com- 
puted by means of the following formulas and tables of 
coefficients, 

in which / = length of weir, in feet; 
H = measured head, in feet; 
v = velocity with which water approaches the weir, 

in feet per second; 
h = head equivalent to velocity with which water 
approaches the weir, or a head that would 
produce a velocity equal to v; 
c = coefficient of discharge; 
Q = actual discharge, in cubic feet. 
The actual discharge for weirs with end contractions is 
given by the formulas: 

Q = 5M7 cl (H+lAh)* (1) 

which is used where the water approaches the weir with a 
velocity equivalent to the height k, and 

Q = bM7 clH* (2) 

where the water has no velocity of approach. 

The actual discharge for weirs without end contractions is 
given by the following formulas: 

Q = 5.347*/ (H+ih)* (3) 

which applies in cases where the water has a velocity of 
approach, and 

Q = 5.347 clH* (4) 

which applies where the water has no velocity of approach. 

47. Velocity of Approach. — By this term is meant the 
velocity with which the water flows through the channel lead- 
ing to the weir. This may be obtained by finding, approxi- 
mately, the amount of water discharged in a given time and 
the area of the cross-section of the channel leading to the 
weir. Then the velocity of approach will be equal to the 
given amount of water divided by the area; or, 



42 



HYDROMECHANICS 



Then, 



A = area of cross-section of channel, in square feet; 
v — velocity of approach, in feet per second; 
Q = quantity of water, in cubic feet. 

A 

Q may be obtained, approximately, by assuming that v is 
equal to zero and applying the formula for the class of weir 

TABLE II 
COEFFICIENTS FOR WEIRS WITH END CONTRACTIONS 



Effective 






Length 


of Weir, 


in Feet 






Head 
















Feet 


.66 


' 


2 


3 


5 


10 


19 


.1 


.632 


.639 


.646 


.652 


.653 


.655 


.656 


•15 


.619 


.625 


.634 


.638 


.640 


.641 


.642 


.20 


.611 


.618 


.626 


.630 


.631 


.633 


.634 


•25 


.605 


.612 


.621 


.624 


.626 


.628 


.629 


•30 


.601 


.608 


.616 


.619 


.621 


.624 


.625 


.40 


•595 


.601 


.609 


.613 


.615 


.618 


.620 


.50 


.590 


.596 


.605 


.608 


.611 


.615 


.617 


.60 


.587 


•593 


.601 


.605 


.608 


.613 


.615 


.70 




.590 


.598 


.603 


.606 


.612 


.614 


.80 






•595 


.600 


.604 


.611 


.613 


.90 






.592 


.598 


.603 


.609 


.612 


1. 00 






•590 


•595 


.601 


.608 


.611 


1.2 






.585 


•591 


•597 


.605 


.610 


1.4 






.580 


.587 


•594 


.602 


.609 


1.6 








.582 


• 59i 


.600 


.607 



Note. — The head given is the effective head, H-\-%h. When the 
velocity of approach is small, h is neglected. 

in question, as given above. Having obtained this quantity 
Q and from it the value of v, the equivalent head h may be 
found by the formula 

h = .01555 v % 
Since v is small with a properly constructed weir, it is 
usually neglected unless great accuracy is required. 



HYDROMECHANICS 



43 



48. Table II gives the values of the coefficients of dis- 
charge c for weirs with end contractions and different values 
of H and /. In this table, the head given is the effective 
head H + i h. When the velocity of approach is small, h is 
neglected and the head becomes simply H, but this change 
will not affect the coefficients in the table. 

Table III gives the values of c for weirs without end con- 
tractions. Weirs with end contractions are more often used 

TABLE III 
COEFFICIENTS FOR WEIRS WITHOUT END CONTRACTIONS 



Effective 






Length 


of Weir, 


in Feet 






Head 
















Feet 


19 


10 


7 


5 


4 


3 


2 


.10 


.657 


.658 


.658 


.659 








.15 


.643 


.644 


.645 


.645 


.647 


.649 


.652 


.20 


.635 


.637 


.637 


.638 


.641 


.642 


.645 


•25 


.630 


.632 


.633 


.634 


.636 


.638 


.641 


•30 


.626 


.628 


.629 


.631 


.633 


.636 


.639 


.40 


.621 


.623 


.625 


.628 


.630 


.633 


.636 


.50 


.619 


.621 


.624 


.627 


.630 


.633 


.637 


.60 


.618 


.620 


.623 


.627 


.630 


•634 


.638 


.70 


.618 


.620 


.624 


.628 


.631 


•635 


.640 


.80 


.618 


.621 


.625 


.629 


.633 


.637 


.643 


.90 


.619 


.622 


.627 


.631 


.635 


.639 


.645 


1. 00 


.619 


.624 


.628 


.633 


.637 


.641 


.648 


1.2 


.620 


.626 


.632 


.636 


.641 


.646 




1.4 


.622 


.629 


.634 


.640 


.644 






1.6 


.623 


.631 


.637 


.642 


.647 







Note. — The head given is the effective head H -f f h When the 
velocity of approach is small, h may be neglected. 

and are to be recommended in most cases. Values of c cor- 
responding to values of H and / between those given in the 
tables can be found by interpolating or taking an average 
between the desired figures, assuming that the variation is 
uniform between the values given. In Table III, the head 



44 



HYDROMECHANICS 



given is the effective head H + i k } which, when h is neg- 
lected, becomes simply H. This does not affect the value 
of the coefficient in the table. 

TABLE IV 

CUBIC FEET DISCHARGED PER MINUTE FOR EACH INCH 

IN LENGTH OF WEIR FOR DEPTHS FROM 

1-8 INCH TO 25 INCHES 



Inches 




1 

8 


\ 


3 

8 


1 
2 


5 

8 


3 

4 


7 

8 







.01 


.05 


.09 


.14 


.20 


.26 


•33 


I 


.40 


.47 


.55 


.65 


•74 


.83 


•93 


1.03 


2 


I.I4 


1.24 


1.36 


1.47 


i-59 


1. 71 


1.83 


1.96 


3 


2.09 


2.23 


2.36 


2.50 


2.63 


2.78 


2.92 


3.07 


4 


3.22 


3.37 


3.52 


3.68 


3.83 


3.99 


4.l6 


4-32 


5 


4.50 


4.67 


4.84 


5.01 


5.18 


5.36 


5-54 


5.72 


6 


5.90 


6.09 


6.28 


6.47 


6.65 


6.85 


7.05 


7.25 


7 


7-44 


7.64 


7.84 


8.05 


8.25 


8.45 


8.66 


8.86 


8 


9.10 


9.31 


9.52 


9-74 


9.96 


I0.l8 


10.40 


10.62 


9 


10.86 


11.08 


II. 31 


11.54 


11.77 


12.00 


12.23 


12.47 


10 


12.71 


13.95 


13.19 


13.43 


13.67 


13.93 


14.16 


14.42 


ii 


14.67 


14.92 


15.18 


15.43 


15.67 


15.96 


16.20 


16.46 


12 


16.73 


16.99 


17.26 


17.52 


17.78 


18.05 


18.32 


18.58 


13 


18.87 


19.14 


19.42 


19.69 


19.97 


20.24 


20.52 


20.80 


14 


21.09 


21.37 


21.65 


21.94 


22.22 


22.51 


22.79 


23.08 


15 


23.38 


23.67 


23.97 


24.26 


24.56 


24.86 


25.16 


25.46 


16 


25.76 


26.06 


26.36 


26.66 


26.97 


27.27 


27.58 


27.89 


17 


28.20 


28.51 


28.82 


29.14 


29-45 


29.76 


30.08 


30.39 


18 


30.70 


31.02 


31.34 


31.66 


31.98 


32.31 


32.63 


32.96 


19 


33-29 


33.61 


33.94 


34-27 


34.6o 


34-94 


35.27 


35.6o 


20 


35-94 


36.27 


36.60 


36.94 


37.28 


37.62 


37.96 


38.31 


21 


38.65 


39.00 


39.34 


39.69 


40.04 


40.39 


40.73 


41.09 


22 


41-43 


41.78 


42.13 


42.49 


42.84 


43-20 


43.56 


43-92 


23 


44.28 


44.64 


45.00 


45.38 


45.71 


46.08 


46.43 


46.81 


24 


47.18 


47.55 


47.91 


48.28 


48.65 


49.02 


49-39 


49.76 



49. Table IV gives the quantity of water, in cubic feet 
per minute, flowing over a weir for each i inch of effective 



HYDROMECHANICS 45 

head from i inch to 25 inches, for each inch of length of 
weir. To obtain the quantity of water for any given case, 
multiply the quantity given in Table IV, corresponding to 
the given effective head, by the width of the weir in inches. 

50. To illustrate the use of Table IV, find the volume 
of water discharged per minute over a weir 30 inches in 
length with a head of 3 inches. The quantity of water cor- 
responding to an effective head of 3 inches, is 2.09 cubic 
feet; then multiplying this by the given length of weir 
(30 inches), we have 2.09 X 30 = 62.7 cubic feet per minute. 
When the head is expressed in inches and fraction of an 
inch, the whole number of inches is first sought in the left- 
hand column, and the required quantity of water is then 
found on the same line, in the column indicated by the given 
fraction of an inch. Thus, in the above example, if the 
effective head had been 3i inches instead of 3 inches, the 
quantity of water flowing over the weir would have been 
2.63 X 30 = 78.9 cubic feet per minute. 



MINE DRAINAGE 

Serial 854 Edition 1 

THE HANDLING OF MINE WATER 



SURFACE DRAINAGE 

1. Draining, or unwatering, a mine means the removal 
of the water that accumulates in it. It is a subject that usually 
increases in importance as the mine is developed, since many- 
mines that are dry near the outcrop become more and more 
watery as they increase in depth. The importance of the 
subject is shown by the fact that, in many cases, the weight 
of water pumped out of a mine is many times the weight of 
material hoisted — 30 tons of water being hoisted in some 
instances for every ton of coal mined. The cost of the mate- 
rial produced is thus greatly increased, as the pumping 
charges are usually a dead loss. 

2. Keeping Surface Water From the Mine. — In order 

to keep as much water as possible out of mine workings, pre- 
cautions should be taken at the surface to keep it from 
collecting above the workings or along the outcrop. The 
outcrop of a soft deposit, such as coal, is often distinguished 
by a depression in the surface, which forms a natural sink in 
which the water from the surrounding area collects. This 
collection of water may be prevented by digging a ditch 
along the outcrop to carry off the water. 

It is impossible to absolutely prevent percolation from the 
surface, as part of the rainfall is always absorbed and even- 
tually finds its way into the mine. If water percolates into 
mines from the bed of a stream, it is sometimes possible 

COPYRIGHTED EY INTERNATIONAL TEXTBOOK COMPANY. ALL RIGHTS RESERVED 



2 MINE DRAINAGE 

and advantageous to turn the course of the stream, particu- 
larly if it flows over a mine where the extraction of the 
deposit is likely to disturb the bed of the stream when roof 
falls occur. Where the water from a stream enters a mine, 
and the stream cannot be turned from its course, it may, if not 
too large, be carried over the affected area in wooden flumes. 

3. Flow of Water Into Mines. — The water that finds 
its way into a mine may come from the surface or from 
water-bearing strata overlying or underlying the workings. 
It may enter the mine by percolating through porous rocks, 
through the joints or fissures formed in the strata, or may 
seep in through the bedding planes of the strata, and the 
flow into a mine is often increased by a fall of roof and by 
long-continued and heavy rains. When rain falls on the sur- 
face of the earth, part of the water runs off and part soaks 
into the soil and sinks until arrested by an impervious stratum. 
The amount of water from rainfalls that soaks into the ground 
depends on the contour of the surface and the nature of the 
soil. If there are no depressions, and the surface drainage 
is good, most of the water that falls on the surface will run 
off; but when depressions exist in which the water can collect, 
as in ponds or swamps, gradual percolation will continue over 
the wet area and the water will find its way into underground 
workings, unless the overlying strata are impervious to water, 
or crevices lead it from the workings. The amount of water 
that enters the mine through fissures and crevices in the strata 
depends on the porosity of the strata and the size of the crevices 
through which it passes; crevices permit a large inflow from 
the surface, if they occur in river or lake bottoms, or if they 
pass through water-bearing strata. Faults crossing many 
strata may become channels through which water enters a 
mine. Mineral veins that are formed in fissures are generally 
water bearing, the water following along the vein walls in 
most instances, but sometimes in the vein matter if this has 
oxidized. 

When the strata are of such a nature that underground waters 
can circulate through the crevices, the water may dissolve the 



MINE DRAINAGE 3 

rock and form cavities in which large bodies of water collect, 
at times under great pressure. In the development of a 
mine, the strata left between the excavation and these cav- 
ities may not be sufficiently strong to oppose the pressure, 
in which case the breaking of the strata will cause an inrush 
of water into the mine, and may cause loss of life and dam- 
age to the mine. Where pot holes occur in the measures, 
or where the mine workings are under an old river bed, it is 
customary to systematically test the thickness of the strata 
above the workings by bore holes. 

4. Variation in the Amount of Water. — The amount 
of water entering a mine usually increases as the excavation 
is extended, but not always in proportion to the extent of the 
excavation, since water does not enter in the same quantity 
in all places. Where there are several coal beds being 
worked, the deepest bed frequently contains the least water; 
exceptions to this rule are sometimes found in the anthracite 
fields of Pennsylvania, where the strata have been folded. 

The passage of the water through the soil and rock strata 
is retarded by the effect of capillary attraction, which causes 
the strata to absorb and hold the water in the same manner 
as a sponge. Owing to this, the strata give off little or no 
water until saturated, and the effect of an increase of surface 
water is not felt farther down for a long period. This is 
the reason why the effect of a heavy rainfall is not generally 
felt until some time later, and in deep mines it may be 
wholly unnoticed. The amount of water entering a mine 
also varies greatly in different seasons of the year, the maxi- 
mum amount being usually in the spring. Hence, the appli- 
ances for unwatering the mine must be based on the maximum 
amount and not on the average. 

In working inclined deposits to the rise, the mistake is often 
made of driving so near to the outcrop that caves occur. This 
is bad practice, as it not only injures surface property, but 
allows surface water to drain into the mines whenever it rains 
or snow melts. After hard or continued rains, the surface 
water entering such caves has frequently flooded the mine. 



MINE DRAINAGE 



UNDERGROUND DRAINAGE 

5. Water Level. — The point reached below the outcrop, 

where the surface water does not flow away naturally but 
must be got rid of by artificial means, is termed water level. 
Geologists sometimes term this the level of zinderground waters. 
The method of draining a mine depends largely on whether 
the deposit is flat or inclined, and whether the mining is being 
done above or below water level. Above water level, pump- 
ing is usually unnecessary, except for local depressions or 
swamps, and attention is given chiefly to the location and 
preparation of ditches to carry off the water and to keep it 
out of the way of the workmen and off the haulage roads. 
Below water level, a sump must be provided, to which the 
water is drained and from which it is raised to the surface, 
or to the water level. 

FLAT DEPOSITS ABOVE WATER LEVEL, 

6. Adit Drainage. — An aclit is a nearly horizontal pas- 
sage from the surface, with just sufficient slope to insure 
drainage, and by which a mine is unwatered. The term adit, 
therefore, includes both a drift in the deposit or a tunnel in 
rock across the measures. A flat deposit is a level or 
slightly inclined deposit. Whenever such a deposit can be 
worked through adit levels, it is customary to locate the mine 
opening at the lowest available point on the property where 
the deposit outcrops above water level and then to drive the 
main roads at a slight inclination so as to obtain a fall toward 
the mine opening that will insure natural drainage for the 
greatest possible area. If these adits are to be used as 
haulage roads, they are provided with ditches excavated 
either at one side or underneath the track. Water will run 
in smooth ditches that have a uniform grade of 2 inches in 
100 feet; but it is customary to give them a steeper grade 
than this, because dirt and rubbish will accumulate in them, 
especially on haulageways. The floors of bedded deposits 
seldom have uniform inclinations, but rise and fall in places; 
and it is well to give the ditches uniform grades, irrespective 



MINE DRAINAGE 5 

of the changes of the floor, if possible; but as this may- 
require considerable cutting of bottom rock the drainage is 
often allowed to follow the natural channel, to avoid cutting 
deep ditches in the entry. 

7. Cross-Entry Drainage. — It is also customary, 
wherever possible, to drive the cross-entries to the rise, at 
such an angle with the main haulageways as will afford 
natural drainage. If necessary, ditches are also provided 
along these cross-entries so that any water that enters this 
part of the mine may drain toward the main entry or adit. 
If there are natural rises or sinks in the floor in which water 
accumulates, ditches may be deepened if no other economical 
method can be suggested to drain such areas. 

8. Swamp Drainage. — Swamps in mines are not gen- 
erally deep or wide and, like swamps found at the surface, 
have high and low places, the latter being the water channels. 
When the miner approaches a swamp, the floor commences to 
dip slightly and water comes into the working. When only a 
small quantity of water accumulates, it is bailed into a water 
car and hauled out of the mine on the commencement of each 
shift. If more than three water cars are required before the 
place is in a satisfactory condition for the miner to work, this 
method of drainage is too slow and expensive; and if the 
swamp is a foot or more deep, a hand pump, an electric pump, 
or a compressed-air pump should be used in its place. Such 
pumps are connected with a delivery pipe that leads into the 
nearest ditch and will ordinarily drain a good-sized swamp. 
As soon as the swamp has been passed through and the floor 
of the deposit assumes its regular inclination, no further 
pumping will be necessary since the water that was in the 
swamp channels will, as a rule, flow off in its natural channel 
and not accumulate and overflow into the mine. 

9. Contonr Drainage Map. — It is an excellent plan, 
and one now often followed in coal mines where swamps are 
found, to take their levels and place them on the mine map, 
and to make a contour map of the floor of the bed, as shown 
in Fig. 1. 



6 MINE DRAINAGE 

The general contour of the affected district being thus 
ascertained, it will be possible, in most instances, to cut one 




ditch that will drain the entire troublesome area. A ditch 
here and there, cutting across local anticlinals or high places, 
may bring water from the different drainage areas of the 



MINE DRAINAGE 7 

mine into a main ditch or natural waterway. If the con- 
ditions permit, this waterway may be located near, and 
parallel to, main haulageways, where it will be accessible 
and will be part of a scheme working- in harmony with future 
developments. A map of this character permits a systematic 
drainage system to be laid out, and the use of shorter drain- 
age ditches than would otherwise be obtained. 

10. Drainage of Temporarily Abandoned Mine 
Workings. — It is customary in some systems of mining 
bedded deposits, to leave a certain percentage of the mineral 
as pillars to support the roof, the intention in such cases, 
being to recover these pillars after the boundary line of the 
property has been reached. Such temporarily abandoned 
portions of a mine are likely to have roof falls through 
which water will enter, and accumulate until it overflows into 
the active mine workings. If any inconvenience is antici- 
pated from such areas, they should be thoroughly ditched, 
if the floor is of such a nature as to permit ditching; if not, 
dams must be constructed to retain the water so that it can 
be drawn off and led into proper channels by means of a 
siphon or pump. 

11. Drainage of Robbed Areas. — Whenever the mining 
has reached the boundary of the property and before rob- 
bing is commenced, a deep ditch should be made on the dip 
side of the first panel robbed, to catch the water, which 
will accumulate in ever-increasing quantity as the area of 
crushed roof is widened. This ditch should connect with the 
main drainage ditch, so that the water may be carried away 
by gravity as much as possible. As the robbing will cause 
the roof to fall and probably fill this ditch, it will be neces- 
sary to construct a new ditch for the next lower panel as that 
panel is robbed. In flat-bedded workings with a regular dip, 
such ditches should be made on cross-entries and be com- 
pleted before robbing the panel is commenced. 

It is sometimes possible to drive from the lowest point of 
the outcrop, near the robbed portion of the mine, a tunnel 
that will drain off the water and prevent its backing into the 



8 MINE DRAINAGE 

workings and traveling roads; or possibly a cross-cut tunnel 
may be made to tap accumulated water. It may be possible 
that dams, siphons, or drain pipes attached to dams will 
afford the desired relief; if not, pumps must be used. 

In temporarily or permanently abandoned workings, the 
mine maps showing the contours of an irregular mine floor 
will be especially valuable as data for locating drainage tun- 
nels and ditches. Experience has shown that, where nearly 
flat mineral deposits outcrop, the floor often bends upwards 
similar to the rim of a plate, and that this requires a ditch to 
be deeper at the outcrop than in the mine in order to obtain 
proper drainage. In case the floor of the deposit is fireclay, 
or hard pan, the action of air and water will require the 
ditches to be cleaned regularly if on traveling roads; but 
since this is not possible in robbed workings, it follows that 
the ditches in these places should be wide and deep, so that 
the water will find a passage between the broken rocks 
that fall into them. 

FLAT DEPOSITS BELOW WATER LEVEL 

12. Sumps. — When comparatively flat deposits are 
worked below water level, the haulageways are usually made 
the drainage levels and are constructed with ditches that lead 
to a common catch basin called the sump. Sumps are usually 
excavated near the shaft or incline used for hoisting, so that 
they will be near the column-pipe that passes through these 
openings, and so that the pump suction pipe will not be too 
long. If there are no workings below the pump level, the 
sump may be made directly under the shaft, otherwise it is 
placed to one side of the shaft, sometimes in the deposit and 
sometimes in rock, according to the condition of the strata. 

Where the water comes into a mine at some distance from 
the pump, it may be necessary to provide a local sump and 
to use an auxiliary pump to send the water from this point 
to the main sump; or it may be cheaper to unwater this 
section through a bore hole from the surface, provided 
that the depth is not too great, or through a shaft sunk for 
this purpose. 



MINE DRAINAGE 



For draining water into sumps numerous methods are 
employed besides ditches. If the water accumulates some 
distance from the rise of the sump, it is generally advisable 
to make an auxiliary sump in that locality and pipe the water 
to the main sump, by this means keeping it out of the haul- 
ageways and keeping them dry. When water accumulates in 
small quantities on levels above the sump, it may be con- 
ducted to the main pump sump by pipes. If, however, the 
water is in large quantities on the upper levels, it should not 
be allowed to go to the 
bottom of the mine, but 
should be caught in 
auxiliary sumps and 
pumped from them to 
the water level, or to 
the surface. This may 
require several auxiliary 
sumps on the upper 
levels, but if the quan- 
tity of water is large 
they will soon pay for 
their construction by the 
lower cost of pumping 
from the higher levels. 



13. Shaft Lodg- 
ment.— In the case of 
shaft mines, as much as 
possible of the water that would naturally drain into the shaft 
from wet strata penetrated by it should be kept out of the 
shaft by lodgments, as shown in Fig. 2. The water caught 
in these lodgments may be pumped to the surface, either by 
a pump placed at the lodgment or it may be piped to an 
auxiliary sump located below the lodgment. Where several 
flat deposits are worked from the same shaft, the water from 
each deposit should, when possible, be caught in a sump 
placed in the rock at the level of the deposit and not allowed 
to drain to the bottom of the shaft. Fig. 3 shows such an 




Pig. 2 



MINE DRAINAGE 11 

auxiliary sump a placed at the mine level, into which water 
is drained either from a lodgment or from a level above, and 
from which it is pumped by a triple-expansion pump b con- 
nected with a condenser c. The pump draws its water from 
the sump through the pipe d and discharges it through the 
column-pipe e. The steam for the pump comes from the sur- 
face and is admitted to the high-pressure steam cylinder by 
the valve / and escapes from the low-pressure steam cylinder 
through the exhaust pipe g into the condenser c. The water 
for the condenser comes from the lodgment, or level above, 
through the pipe h and, passing through the condenser, flows 
through the pipe i into the sump. The pipe h is equipped 
with a valve j that regulates the quantity of water flowing 
into the sump, without cutting off the supply needed for the 
condenser, by means of a float k, rod /, and lever m attached 
to the valve stem. As the float falls, the lever opens the 
valve and permits water to flow into the sump; as the float 
rises, the lever closes the valve, thus cutting off the flow. 

Example 1. — Suppose that a mine is 600 feet deep, what power 
will be saved if 1,000 cubic feet of water is pumped to an adit 100 feet 
below the shaft head rather than to the shaft head? 

Solution. — The power required to lift the 1,000 cu. ft. of water 

mn , . , . . . 1,000X62.5X600 , ro£i oa __ _ _, 

600 ft. in 1 minute is, ^ = 1,136.36 H. P. The power 

required to lift the same amount of water to the adit, or 500 ft., in 

1 000 X 62 5 V 500 
the same time is, 33 000 = 946 " 97 H ' P " The savin 2' with_ 

out considering the usual 20 percent, additional power for friction, will 
be, 1,136.36 - 946.97 = 189.39 H. P. Ans. 

Example 2. — Suppose that in example 1 all the water came from 
near the surface and could be caught in a sump at a level 200 feet below 
the surface; what power would be saved by so doing, and not allowing 
the water to go to the bottom of the shaft? 

Solution. — In example 1, it was found that 1,136.36 H. P. is required 
to pump 1,000 cu. ft. of water from a depth of 600 ft. in 1 minute. 
The power that would be required to pump the same amount of water 
in the same time from the 200-ft. level is, 

1, 000 X 62.5 X 200 

33^000 = 378 ' 78 H - R 

The saving will be 1.136.36 - 378.78 = 757.58 H. P. Ans. 



12 



MINE DRAINAGE 



INCLINED DEPOSITS ABOVE WATER LEVEL 

14. Adit Drainage. — Adits in inclined deposits are 
suitable for draining all the deposits above them. Drainage 
ditches should be placed either on the side or beneath the 
roadway, and should have a uniform grade of not less than 
4 inches, or more than 8 inches, in 100 feet, the grade being 
governed by that given the roadway. The ditch should, in 
most instances, be on the foot-wall side of the deposit as 
shown in Fig. 4, as then it will not be necessary to break the 

hanging wall, and water will 
not be so apt to drop into the 
roadway and keep that wet. 
Further, whatever water may 
trickle or run down the hang- 
ing wall can be led across the 
adit to the ditch side and be 
drained off. When the deposit 
is worked below the adit 
level, if the ditch is made on 
the foot-wall side of the 
deposit, most of the water 
will drain off through the adit 
and not be troublesome in the 

Fig. 4 , , . 

lower workings. 
If the deposit is wide and it is not necessary to break either 
the hanging wall, or foot-wall, for passage room, the ditch 
should be placed on the foot-wall side. If the greater part 
of the water comes from the hanging-wall side, it may be 
necessary to place ditches on each side of the adit, but the 
main ditch should be on the foot-wall side, with the ditch on 
the hanging-wall side answering as a gutter or leader to the 
main ditch. It may not be necessary to carry the ditch on 
the hanging-wall side the entire length of the adit, since 
extremely wet places are local; but where they occur the 
gutter leading to the main ditch will be found a great con- 
venience, and very economical where there are lower 
workings. 




MINE DRAINAGE 



13 



15. In some instances, the ditch in an adit is made 
beneath the track, as in Fig - . 5. In wide deposits, this is not 
objectionable if, for some reason, it is not desirable to work 
close to the foot-wall, but the chances for the water that runs 
in the ditch going to the lower levels are much increased 
when ditches are so arranged, unless the deposit is tight or 
practically impervious. In an adit of small area a center 
ditch may be necessary on account of weak walls or close 
timbering. When conditions are favorable for side ditches, it 
is bad and expensive practice to use a center ditch, since the 
cross-ties must be planked 
over and this covering kept 
in good order. Another dis- 
advantage is that ditches be- 
neath a track cannot be reg- 
ularly cleaned without con- 
siderable extra labor and 
expense for the removal and 
replacement of the plank 
covering. 

16. Drainage Tunnels. 
Drainage tnnnels are tun- 
nels driven to tap a given 
mine or mining district below 

the natural water level of the district. Such tunnels have been 
driven 1,700 feet below the shaft mouth and many miles 
long. The Sutro tunnel, in Nevada, was excavated for the 
purpose of unwatering the mines on the Comstock lode. 
It was driven with great difficulty because of the extreme 
heat of the rocks and water, and the swelling ground, which 
broke the strongest timbers, and because 45.5 per cent, of 
the entire length required timbering. The water in this 
tunnel is carried in a ditch cut in the tunnel floor; it amounts 
to 12,000 tons daily, and has a temperature of 123° F. when 
it leaves the tunnel mouth. To pump this water to the 
surface, before the tunnel was constructed, cost $3,000 per 
day. 




14 MINE DRAINAGE 

Occasionally, the owners of several mines club together 
and build drainage tunnels, or a corporation is formed for 
the purpose of tunneling to unwater several mines, such as 
the Aspen Tunnel Company, at Aspen, and the Wooster 
Tunnel, at Creede, Colorado. These tunnels may also be 
used as haulageways, while the companies become owners of 
any veins they discover in driving the tunnel. 

Tunnels for drainage purposes, to be of much practical 
value, must be driven at a considerable depth below the 
mouth of the mine. This is expensive work in barren 
ground, and all advantages to be derived from their excava- 
tion should be well considered. It is not advisable to drive 
a drainage tunnel to meet a mineral deposit that has not 
been previously prospected to a depth equal to that of the 
proposed tunnel level, if the value of the deposit is to defray 
the cost of driving, for there is no surety that the mineral 
will continue to that depth. Experience has taught that 
cross-cut tunnels are not to be driven haphazard, and that 
their usefulness should be determined from known rather 
than supposed data. There are a number of instances on 
record where cross-cut tunnels were driven at great expense 
to cut mineral deposits which petered out or were faulted 
before the tunnel depth was reached. 

17. The Jedclo tunnel, in the Black Creek anthracite 
basin of Northeastern Pennsylvania, is about 5 miles long, 
extending from Black Creek under the intervening hills to 
Butler Valley, Black Creek Valley is at a considerably 
higher altitude than Butler Valley, hence it was possible 
to tunnel under the coal beds and drain the mines above 
and below the Black Creek level. The mines in Black Creek 
Valley, previous to the construction of the tunnel, suffered 
from the waters of Black Creek draining into them and 
several times some of them had been flooded. This tunnel, 
however, drained the area most affected and helped the other 
area, thus making large quantities of first-class coal available 
for market. The line of the tunnel having been mapped out, 
two slopes were sunk to give five headings to the tunnel and 



MINE DRAINAGE 



15 



so expedite the work. The tunnel was 7 feet by 11 feet in 
sectional area and, by the use of compressed-air drills, was 
driven at a rapid rate, 308 feet being driven in one heading 
and 301i feet in another during May, 1894. 



INCLINED DEPOSITS BELOW WATER LEVEL, 

18. Sumps are placed in the mine as was described in 
Art. 12. Sumps on upper levels should be dug in the foot- 
wall and be cemented to make them water-tight in order 
that no water may run back to the next lower pumping 
station. If the sump is to act merely as a catch basin for 
the pump below, a large wooden tank may answer every 
purpose; but where the sump is located in the deposit, or in 
seamy country rock, and not made water-tight, leakage will 
occur and the water will have to be raised from a lower level. 




19. Ditches on Levels. — The main drainage ditches 
in inclined deposits are on the 
levels that are driven right and 
left from the pump shaft, or 
slope. The position of the 
ditch on the level depends on 
the position of the level with 
respect to the deposit. These 
levels are driven in the deposit 
wherever the conditions will 
permit; and when that is not FlG-6 

possible, they are driven partly in the deposit and partly in 
the country rock, or sometimes entirely in the country rock. 
They are given a uniform grade varying from 2 inches to 
8 inches in 100 feet; the latter, however, is excessive for most 
cases. Fig. 6 shows a level driven entirely in the deposit, 
with a ditch on the foot-wall side, the mineral in this case 
being firm enough to stand without timber, besides carrying 
little water. 

Fig. 7 shows a level driven entirely in the deposit, which 
must be supported overhead by timbers. In this case, the 



16 



MINE DRAINAGE 



ditch is on the foot-wall side. Fig. 8 shows a level driven 
partly in firm vein rock and partly in rather weak country 
rock, the ditch, in this case, being placed on the foot-wall. 
There are numerous other situations in which levels may be 
driven, but it is usually advisable to place the ditch on the 
foot-wall side. 

In a situation similar to that illustrated in Fig. 9, where 




the ground is weak on all sides and requires timber sets for 
its support, the ditch is necessarily placed below the sills; 
but in such a case as shown in Fig. 10, where only the 



T-C. •■'-•;* 




deposit is weak, the ditch is probably located best away 
from the bed, water being drained to it by local gutters. If 
the roof is water bearing and the deposit is not, the ditch 
should generally be placed on the hanging-wall side, thus 
making an exception to the regular rule. 



MINE DRAINAGE 17 



DRAINAGE OF WORKING PLACES 

20. Room Drainage. — In working flat seams, it often 
happens that the drainage, though slight, is toward the 
working face instead of toward the mouth of the room, 
where the water would be discharged into the ditch along 
the entry. When water drains toward the mouth of the 
room, little care on the part of the miner is required; but 
when the water drains toward the face, recourse must be had 
to the water car and bailing, to remove the water from the 
face of the rooms. If there is an excessive amount of water, 
which would delay work at the face, it is sometimes advan- 
tageous, or even necessary, to excavate a small sump at the 
lowest point of the face by placing a light shot in the 
bottom. 

In working inclined seams, rooms are seldom driven to the 
dip of the seam, and hence little trouble is experienced in the 
drainage of the working face. Care, however, is required in 
all inclined workings to prevent, as far as possible, the water 
in one level from finding its way into the workings below. 
To accomplish this, a continuous chain pillar is maintained 
on the lower side of each level or gangway, and careful 
measurements are taken in each room to avoid driving the 
rooms from below up through this pillar; or, sometimes, to 
prevent any possibility of the rooms driven up from a lower 
level breaking through the chain pillar, a cut-off room is 
driven parallel to, and just below, each level. The entry 
ditch in each level is carried on the side of the roadway up 
the pitch, that is, on the foot-wall side, to prevent the water, 
as far as possible, from seeping under the pillar dividing 
this level from the workings below, as would naturally be 
the case if the ditch were carried on the opposite side of 
the entry. 

21. Drainage in Stope Mining. — In stope mining, 
continuous pillars with ditches are not always left to carry 
the water away from the miner working below. Therefore, 
-where there is much water to contend with, at certain 



18 



MINE DRAINAGE 



intervals winzes are sunk from one level to another, or raises 
are driven from one level to a level above, in order to drain 
the water from the stope. If the level is one on which there 
is a pump, a chain pillar should be left below the level and 
arrangements made to carry the water over any hole made 
through this pillar from below. If there is not a pump on 
the level, all water should be led as directly as possible to a 
lower level away from working stopes, where it would cause 
inconvenience to the men. In underhand stoping, the water 
follows the stopes, often making ore and tools wet; but in 
overhand stoping, the men in the upper stope are more incon 
venienced by water than those on lower stopes. 



TAPPING AND DRAINING ABANDONED WORKINGS 

22. When exploitation has reached the boundary line of 
a property and the mine has been robbed back and aban- 




doned, water is likely to accumulate until the mine has filled. 
If other mining operations are approaching this abandoned 
property, all entries should be carefully driven narrow and a 
bore hole pushed at least 20 feet in advance of the face, and 
similar bore holes to flank each side. Bore holes 20 feet 
long are not considered by some to be a sufficient safeguard 
in a thick seam or on steep dips, but this must necessarily 
depend on the depth of the water and the strength of the coal. 



MINE DRAINAGE 



19 



By disregarding such simple precautions, and because records 
of old mine excavations have not been kept or examined, a 
number of accidents that have caused loss of life, as well as 
serious damage to mining property, have resulted. Some 
state mine laws require that duplicate surveys be made 
before a mine is abandoned and these surveys must agree 
and be accurately plotted on a map. A certified copy of 
this map is then filed with the mine inspector of that par- 
ticular district. 

Fig. 11 shows the risk run in approaching old workings 
known to exist but not surveyed and mapped. The gang- 
way a was being worked in 
coal, and it was thought advi- 
sable to cross-cut to reach 
another bed that had been 
worked and in which at this 
depth there would be a head 
of 150 feet of water. The 
diamond-drill hole b was 
drilled from the cross-cut 
heading at a 33° pitch, but no 
water was struck. The hole c 
was next drilled at a 70° pitch, 
so as to cut the seam at nearly ^ Pi =^==^^ :i: -^ :=rS: ~ 

right angles; this hole gave F10.12 

some water, but no absolute position of the old workings, 
and was as unsatisfactory as the first. The hole d was next 
drilled vertically about 3 feet back of the hole c, so as to reach 
the coal; this struck into old workings, but did not show water 
until within 2 feet of them. 




23. Draining Off Water. — If the bore hole taps a 
body of water in an abandoned mine, a larger hole is drilled 
into the face and a pipe a is inserted into the face 4 or 5 feet, 
as shown in Fig. 12. Through this pipe, a hole b of smaller 
diameter is bored until the water is reached. A valve c, with 
an extension d, is placed on the pipe and fastened to a heavy 
prop e to prevent the water from blowing out the pipe when 



20 MINE DRAINAGE 

the valve is turned off. The object of this arrangement is 
to drain off the accumulated water gradually and not let it 
flow in such quantities as to flood the mine. This arrange- 
ment has also been adopted to prevent the water in an 
abandoned mine rising to a height that would endanger the 
barrier pillar. 

24. Tapping a Body of Water From Below. — In 
the following case, a cross-cut tunnel was driven to tap a 
body of water above the tunnel. In driving toward the 
water, flanking holes and horizontal holes were driven ahead 
of the work. When the first hole tapped the old workings, 
12.5 feet of strata remained between the two excavations. 
Twelve diamond-drill holes 10 inches from each other were 
then run into the old works, but on account of their small 
size and the enormous pressure of the water, these holes 
were quickly blocked with sediment so that this plan had to 
be abandoned. 

Long wooden plugs were then driven into the holes and 
each plug pierced by an auger hole, which was charged with 
dynamite and fired with the expectation that the shots would 
break down the barrier. The result was a surprise, as the 
holes simply acted like so many cannon, only a part of the 
plug being broken. Seventy-five pounds of dynamite was 
next placed in holes driven slanting to a depth of about 7 feet, 
the expectation being that the charge would burst through 
the barrier and discharge the water. When the charge was 
fired there was at first a great rush of water, which, however, 
stopped immediately, and then not as much water as would 
flow from one drill hole escaped. It was evident from this 
that the heavy pressure of water had not only counteracted 
the force of the dynamite, but forced the sediment that had 
accumulated in the old workings into the crevices formed by 
the explosion and stopped them up. The coal was so shat- 
tered by the last explosion that it was not deemed advisable 
for the men to work at this place. A second tunnel was then 
driven parallel to the first one, and a vertical rise 4 feet square 
was driven up 6 feet when a dividing slate was reached; then 



MINE DRAINAGE 21 

it was narrowed to 3 feet square through the 10 inches of 
slate, and again narrowed to 2 feet square in the coal bench 
and carried to within 2 feet of the old workings. A prop, 
14 inches in diameter, having on top a 14-inch square iron 
box was so set in this shaft that the box came close to the 
roof of the shaft. The box was partly rilled with dynamite, 
which was fired by electricity. To prevent the prop from 
stopping the flow of water, it was necessary to bore a hole 
in it with an auger, and in this hole a dynamite cartridge was 
fired immediately after the charge exploded in the pan, thus 
breaking down the prop and letting out the water. 

25. Barrier Pillars. — The laws of some states require 
a pillar of coal to be left in each bed of coal worked, along 
the line of adjoining properties, of such width, that, taken 
in connection with the pillar to be left by the adjacent prop- 
erty owner, it will form a sufficient barrier for the safety of 
the employes of mines on either property in case one should 
be abandoned and allowed to fill with water. These pillars 
are known as barrier pillars. The width of such pillars 
is determined by the engineers of the adjoining property 
owners and the mine inspector in whose district the proper- 
ties are located. 

An arbitrary rule for the width of barrier pillars, adopted 
by a number of coal companies and by the State Mine 
Inspectors of Eastern Pennsylvania, is as follows: 

Rule. — Multiply the thickness of the deposit ', iti feet, by 
1 pe?' cent, of the depth below drainage level ', and add to this 
five times the thickness of the bed. 

Thus, for a bed of coal 6 feet thick and 400 feet below 
drainage level, the barrier pillar will, according to this rule, 
be (6 X 400 X .01) +(6x5) =54 feet wide. 

The bituminous mine law of Pennsylvania requires a 
thickness of 1 foot of pillar for each \\ feet of water head, 
if, in the judgment of the engineer of the property and of 
the district mine inspector, this thickness is necessary for 
the safety of the persons working in the mine. 



22 MINE DRAINAGE 

MINE DAMS 

26. Use of Mine Dams, — Dams are built for the fol- 
lowing purposes: to confine water to certain parts of a mine 
in order to reduce the flooded area and the pumping charges; 
to prevent the pumps being flooded when the inflow of water 
to the mine is excessive in wet weather; for the purpose of 
flooding the whole or a part of a mine to extinguish a mine 
fire; and to keep back deleterious gases given off in old 
mine workings. They are made of wood, brick, stone, or 
concrete and should be provided with drain pipes near the 
floor, a manway near the center of the dam, and an air escape 
for air or gases close to the roof. The drain pipes and air 
vents are furnished with valves or cocks to regulate the flow. 

Dams in mines necessarily differ from those constructed 
above ground, since nearly every square foot of the sur- 
face of a mine dam exposed to the water is subjected to 
practically the same pressure. The principal requirements 
of a mine dam are that it shall be water-tight and capable of 
resisting the pressure of a given head of water. Before the 
dam is planned, a full understanding of the attending con- 
ditions must be had; as, for example, the surroundings in 
which it will be located and what the pressure against it will 
be. These data are necessary in order to calculate the 
required strength of the dam and to determine its form and 
thickness and the material for its construction. 

27. Location of Dams. — The site chosen for a mine 
dam should be such that the junction between the sides of 
the excavation and the material of the dam can be made 
water-tight, since a small leak may increase to such propor- 
tions as to endanger the entire work. A dam should have 
solid-rock sides, top, and bottom wherever possible; if this 
is not possible, rock roof and bottom are the next most 
desirable; but in case the deposit is on a pitch, it may be 
necessary to place the dam partly in the deposit and partly 
in rock. The sides of the excavation against which the dam 
abuts will need more care if they are in the deposit than if 



MINE DRAINAGE 



23 



in solid rock, particularly if the width of the dam is to be 
greater than its height. 

Dams should be located in an accessible place, where they 
may be easily inspected and where subsequent mining will 
not disturb their stability 
or that of the walls to 
which they are tied; they 
should be built in a nar- 
row place, if such is 
available. 

28. Water Pressure 
on Dams. — The pressure 
against a dam is equal to 
the rectangular area of the 
face of the dam against 
which the water presses 
multiplied by the mean 
head of water, in feet, and 
by 62.5 pounds, the weight 
of a cubic foot of water, 
when the area is expressed 
in square feet; or by .434 
pound, the weight of 12 
cubic inches of water, when 
the area is expressed in 
square inches. The mean 
head used is the vertical 
distance from the center of 
the dam to the surface of 
the water. Thus, if a mine 
is flooded and the vertical 
depth of the water is 100 
feet, the pressure per 
square foot at the bottom is equal to the weight of 1 cubic 
foot of water multiplied by the depth, in feet, or 100. Hence, 
62.5 X 100 = 6,250 pounds per square foot. At a point half- 
way down, the water will press against the sides with a 




24 MINE DRAINAGE 

pressure equal to -HP X 62.5 pounds = 3,125 pounds per 
square foot. 

Example. — What pressure must a mine dam that is built across a 
gangway 10 feet wide and 6 feet high withstand, when the water in 
the mine can rise to a point 203 feet vertically above the floor of the 
gangway? 

Solution. — The area of the face of the dam is 10 X 6 = 60 sq. ft. 
and the mean head is 203 — f = 200; therefore, the pressure against 
the dam is 60 X 200 X 62.5 = 750,000 lb. Ans. 

29. Dams to divert the course of water are subjected to 
little or no pressure and may therefore be an ordinary wood, 
brick, or stone stopping with water-tight joints. A dam of 
this nature may be constructed of two walls of plank sup- 
ported by props firmly fixed in the top and bottom and with 
the space between filled with puddled clay, or, better, with 
concrete. The joints of the planks should be battened on 
the side next the water. Fig. 13 shows a plan (a) and 
section (b) of such a dam, in which a are posts; b, planking; 
c, battens; and d, the puddled clay, which is from 1 to 2 feet 
thick. The small pipe near the top permits the air to escape 
while the water is rising. The large pipe at the bottom is 
for draining ofT the water. 

30. Wedge-Shaped Wooden Dam. — Fig. 14 shows a 
wedge-shaped dam that may be applied in most cases 
where no other dam can be effectively placed. This dam con- 
sists of sections of wood, carefully dressed with a taper, and 
placed with the thick end next the water. The taper of each 
piece depends on the radius of the curvature of the dam and 
is greater for a dam with a small radius than for one with a 
large radius. Each timber should be properly numbered, so 
that when the separate pieces are taken into the mine they 
can be placed in their proper positions. Thoroughly dried 
timber should be used, as that will swell when wet and 
tighten the joints. The lengths of the tapered pieces, or the 
thickness of the dam, will depend on the pressure that tne 
dam is to resist and may vary from 3 to 8 feet. Notwith- 
standing the most careful wedging, the pressure on the face 
of such dams is sometimes great enough to move the whole 



MINE DRAINAGE 



25 



structure; therefore, it is advisable to dress the sides of the 
passage in such manner that the pressure will tend to wedge 
the structure tighter. 

While the dam is being constructed, it is necessary to 
insert iron pipes about a foot from the bottom, of sufficient 
size to carry off the 
water that would 
otherwise accumulate 
and prevent the com- 
pletion of the work. 
In Fig. 14, a is a drain 
pipe; b is a manhole 
which is about 18 
inches in diameter and 
2 feet from the bot- 
tom, and permits the 
ingress and egress of 
the workmen during 
the construction and 
wedging of the dam. 
A pipe c, from 3 to 6 
inches in diameter, 
placed near the top, 
and provided with a 
valve, allows the air 
to escape while the 
water is rising. If at 
any time it is desired 
to draw the water off 
slowly, this valve can 
be opened. FlG - 14 

The sides of the excavation for the dam should be lined 
with tarred flannel, so as to form a water-tight joint with the 
timbers. The tapered timbers are next placed in proper 
position, and dry wooden wedges, 12 inches long and 3 inches 
by 1 inch at their heads, are driven between the joints. 
Smaller wedges are driven around the pipes, as long as they 
can be entered, after which a chisel is used to prepare places 




26 



MINE DRAINAGE 



for their insertion. When the wedging is h/iished, the work- 
men drive the plug e into the pipe a through which the water 
has been flowing. They then pass through \he pipe b, 
drawing into place the plug d, which has been placed con- 
venient for so doing, and by this means stop up the man- 
hole. It is stated that dams of this description, constructed 
of first-class wood free from defects, will resist a pressure 
of 260 pounds per square inch. Other designs for wooden 
dams have proved effective, but all depend on good work- 
manship in construction, as well as on design. 

31. Flat Wooden Dams. — Fig. 15 shows the plan of a 




wooden dam erected in a colliery to hold back water when 
the mine was flooded to extinguish a fire. The tunnel was 
10 feet by 7 feet, in section, and notches 3 feet deep were 
cut in each rib and in the bottom. About each end of the 
timbers forming the dam, brick were laid in cement. The 
inside timbers were yellow pine while the two back timbers 



MINE DRAINAGE 



27 



were oak. When placing the first two rows of timbers, a 
manhole a made in keystone shape was used, but this was 
blocked up and bolted before the oak timbers were placed. 
The drain pipe b extended through the four timbers and was 
supplied with a cock c and a pressure gauge. This structure 
was reenforced by the posts d, the tie e, and the braces / 
fitted together as shown. These timbers were placed one 
on top of the other from the floor to the roof, and the 
braces / fitted and wedged into notches in the sides of the 
tunnel. 



32. Brick Dams. — The brick dam shown in plan in 
Fig. 16 has a maximum radius of 30 feet and a thickness of 
15 feet from a to b. 
These dams are con- 
structed to wooden tem- 
plets, termed centers, 
which are placed in 
position before the 
brickwork is com- 
menced, and by the use 
of these centers, the 
exact radius and the 
proper curvature can be 
followed by the masons 
better than by the use of - 

the long sweeps that H \\\ //'' 

would otherwise be re- I \\\ //,. 

quired for determining I \^ //('' 

the curvature of the ^^^^ \ y 

wall. The arches FlG ° 16 

marked by the arcs c d, 

ef, andg-k are skewed into hitches cut in the walls so as to 
form skew-backs, thereby increasing the strength of the arch 
as the pressure is increased. These hitches receive the pres- 
sure in such manner as to produce an inward thrust and thus 
reduce the liability of breaking out the walls. The radius of 
curvature for masonry dams depends on the pressure to be 




28 MINE DRAINAGE 

resisted and the size of the opening. The dam is provided 
with a manhole i, an air vent /, and a pipe k for draining- off 
the water. 

33. Fig. 17 shows a plan of a dam built of two spherical 
brick arches a, b from 6 to 12 feet apart, the space between 
being filled with puddled clay, or, better, with concrete. This 

form of dam is suitable: 
where the resisting, 
walls are soft. Pipes 
are inserted in these 
dams, as in wooden 
dams, and for the same 



r'Z 




,.<'">-<> r|MiB'--v reasons. 

;■■-;: :;: 34. Fig. 18 shows 

'4^&^^^^^^^^ a V^ an ^ anc * vert ical 

section (b) of a liori- 

^>/ i y^o-^VtS'^ 1 ^iV'7-i^B z o n t a 1 brick dam 

*£Mm&- m^wU ' built at a colliery to 

shut off a large inflow 
of water from the roof 
close to the face of a 
chamber. As there 
/ j was considerable depth 

/ of wash, or drift, over 

\ / | the seam, it was; 

thought advisable to 
abandon, for a time, all. 
mining at that level 
until the coal below was worked out. The dam was made 5 feet 
thick, of brick laid in cement, and its length from pillar to 
pillar was 25 feet, arching from bottom to top. In the figure, 
a is a cast-iron pipe for the escape of water while the dam is 
being constructed; b, a tapered white-pine plug turned to fit 
the pipe; d, a manhole used by the workmen as an escape 
after having finished the dam on the inside and having driven 
the plug b; v is the smaller air vent. The soft stratum 



\ 



/ 



MINE DRAINAGE 



29 





(V 

Fig. 18 



immediately under 
the coal was cut away 
and the brickwork 
skewed into the 
harder stratum. This 
dam is formed of 
separate cylindrical 
arches, each of which 
is skewed into the top 
and bottom; and built 
across the passage- 
way, because it would 
be more expensive to 
arch a wide dam longi- 
tudinally. Concrete c 
was placed at the front 
and back of the dam 
where the soft bottom 
has been taken up. 

35. Stone Dams. 
Fig. 19 illustrates the 
plan (a) and cross- 
section (5) of a dam 
in the Curry Iron 
Mine, at Norway, 
Michigan, construc- 
ted to keep the water 
that came from some 
exploring drifts out of 
the mine workingst 
Originally, it was 
constructed of sand- 
stone 10 feet thick 
and arched on the 
face with a radius of 
6 feet. A piece of 
20-inch pipe a held in 



30 



MINE DRAINAGE 



place by three sets of clamps and bolts £ passing through the 
stonework provided a manhole through the masonry. A 5-inch 
drain pipe c was also carried through the dam and secured by 
clamps. When the pressure came on it, the dam was found to 
leak, so the water was drained off and a 22-inch brick wall 

built 2 feet 4 inches 



back of the dam, the 
space between being 
filled with concrete; 
the manway and drain 
pipe were extended 
through the concrete 
and brick wall. Be- 
fore closing the drain 
pipe, stable refuse 
was spread against 
the face of the brick 
wall and covered over 
with planks to hold it 
in place. After the 
manway and drain 
pipe were closed and 
the pressure came on 
the dam, it was again 
found to leak a little, 
but this soon practi- 
cally ceased, showing 
that the stable refuse 
had closed the leaks. 
A pressure gauge in 
the head of the man- 
Fig. 19 hole a registered 211 

pounds pressure per square inch, which corresponds to a head 
of water of 486 feet. The total pressure against the dam 
was over 800 tons, which it successfully resisted. 





36. Shaft Dams. — Abandoned shafts that pass through 
water-bearing strata or permit surface water to flow into a 



MINE DRAINAGE 



31 



mine, may be closed by an arch of masonry, as shown in 
sectional elevation in Fig. 20. The centers a in this par- 
ticular case are made heavy and permitted to remain in 
place, since the dam can be examined from the stringers b 
on which they rest. Above the centers, the brick arch c 
is shown firmly skewed to the sides of the shaft. While the 
masonry is sufficiently strong to resist the pressure that 
will come on it, it may leak; and since water under heavy 
pressure will cut away 
metal, it is always bet- 
ter to puddle such 
structures with clay d 
tightly rammed down 
in order to assure 
water-tight work. To 
prevent the clay being 
disturbed by anything 
that may fall down the 
shaft, it is covered by 
stone e laid in courses 
as shown. This stone 
is further intended to 
prevent the clay being 
washed away in case 
any movement takes 
place in the shaft strata 
which might crack the 
brickwork. During pig. 20 

the construction of the dam, the pipe / drains off the water 
that is caught in a temporarily constructed lodgment above 
the work, and it will afterwards answer for draining off the 
water in the shaft if for any reason it becomes necessary to 
remove the dam or make repairs. 




37. Thickness of Mine Dams. — The cost of the mate- 
rials used in constructing a mine dam is small compared 
with the importance of the work, so that it is not necessary 
to consider the thickness of the dam as affecting the amount 



32 MINE DRAINAGE 

of materials used in its construction. The essential qualifi- 
cation is that the dam shall be amply strong, and for this 
reason it is usually built very much stronger than theoretical 
calculations may call for, and when formulas are used for 
calculating the thickness a large factor of safety should be 
used in the calculation. Several writers have given formulas 
for calculating the thickness of a dam, but the following, 
given by Combes, seem to be the most satisfactory. 

1. For straight dams, where the ends of the dam are laid 
in a straight hitch in the ribs and no attention is given to 
the end thrust against the ribs, the thickness of the dam may 
be calculated by the ordinary formulas for a beam supported 
at both ends and uniformly loaded. 

2. For cylindrical dams, the formula derived from that 
given by Combes is 

T = .868 — (1) 

P 
in which T = thickness of dam, in feet; 

r = shorter radius of dam, in feet; 
h = head of water, in feet; 

p = allowable compressive strength per square 

inch of material used in building dam. 

Example 1. — What should be the thickness of a concrete cylindrical 

dam, with a shorter radius of 10 feet, to withstand a pressure due to a 

head of 100 feet of water, assuming the allowable compressive strength 

of the concrete to be 100 pounds per square inch? 

Solution. — Substituting in formula 1 the values given in the 
example, 10 X 100 

T = .868 X — ~^ = 8.68 ft. Ans. 

3. For a spherical dam, the formula given by Combes is 



4 



wp__ (2) 



!l0p - 4.34 h 
in which T = thickness of dam, in feet; 

r = shorter radius of dam, in feet; 
h — head of water, in feet; 

p = allowable compressive strength per square 
inch of material used in building dam. 
Example 2. — What should be the thickness of a concrete spherical 
dam, with a shorter radius of 10 feet, to withstand a pressure due to 



MINE DRAINAGE 



33 



a head of 100 feet of water, assuming the allowable compressive 
strength of the concrete to be 100 pounds per square inch? 

Solution. — Substituting the values given in the example in for- 
mula 2, 

T - 



•=10^ 



10 X 100 



10 X 100 - 4.34 X 100 



10 = 13.29 - 10 = 3.29 ft. Ans. 



SIPHONS 

38. In many cases, water collects at some point in a 
mine lower than the main drainage ditches but higher than 
the level of the water in the sump, or some place where it 
may be dammed back from the workings. As it is not 
always desirable or expedient to cut a ditch deep enough to 
drain off this water, a siphon may often be used to carry it 
over the high point. 

The principle on which the siphon works is illustrated in 
Fig. 21. A bent tube c filled with 
water is inserted into a vessel a con- 
taining water, the atmospheric pres- 
sure and the difference in the heights 
of the columns of water ec and cd 
will force the water in a to flow 
through the tube into the vessel b. 
The water will continue to flow 
through the tube as long as the 
water in b is below the level of the 
water in a, and the end of the tube 
is submerged in the water in a. 

The atmospheric pressure on the 
surfaces a and b tends to force the 
water up the tubes ac and be; but Fig. 21 

when the siphon is filled with water, this tendency is opposed 
by the pressure of the water in each leg of the siphon. The 
atmospheric pressure on the longer leg b c is therefore opposed 
by a greater force than the atmospheric pressure on the 
shorter leg ac and as a result the water will flow from a to b. 
As the shorter leg is kept full by atmospheric pressure, the 
height to which the water may be raised at sea level is, 




34 



MINE DRAINAGE 



theoretically, about 34 feet, but practically it seldom exceeds 
about 28 feet. 

39. Fig. 22 shows a siphon working in a mine where it 
is desired to convey the water from D to E, the level of the 
water in E being always lower than in D. The siphon con- 
sists of ordinary iron pipe fitted with three valves A, B, and C. 
On the suction end of the pipe, there is a perforated boot that 
keeps out chips and dirt, which might clog the pipe and pre- 
vent the siphon from working. In order to start the siphon, 
it is necessary to fill the pipe, which is done by closing the 
valves A and B, opening the valve C, and pouring water into 
the funnel E; the air is thus driven out from the pipes 




through the funnel. When no more water can be poured in 
without overflowing at E, the valve C is closed, and the 
valves A and B are opened, when the water in the siphon 
will commence to flow. 

40. Fig. 23 shows a very convenient method of filling 
the pipe with water when the siphon is used to carry the 
water from a local sump M to the main sump E. s is the 
height of suction; h, the head that induces the flow; 
A, the valve at the suction end; B, the valve at the delivery 
end; H, the column pipe of the main pump; C, a small pipe 
leading from the column pipe to the siphon, communication 
being opened or closed by aid of the valve D\ K, a chamber 



MINE DRAINAGE 



35 



into which the air escapes when the pipe is being filled; and/,, 
a valve that controls the communication between the siphon 
and the air chamber. In order to keep the air from getting 
past the valve L when it is closed and destroying the action of 
the siphon, the chamber K is kept filled with water. A rod G 
fastened to the short arm of the lever F has attached to it 
the handles of the valves B and D, and the weight /. When 
in the position shown, the valve B is open and D is closed. 
In order to start the siphon, the valve A is closed and L is 
opened. The lever Fis then pulled down; this action raises 
the handles of the valves D and B to the position shown 




Fig. 23 

by the dotted lines, opening the valve D and closing the 
valve B. The water flows into the siphon from the column 
pipe through the small pipe C. When the siphon is filled 
and the water appears at chamber K, the valve L is closed 
and the lever F is released, the weight / pulling it into the 
position shown, thus closing the valve D and opening the 
valve B. The valve A is then opened and the siphon is in 
working condition. 

41. Air in a Siphon. — In order that a siphon shall 
work properly, it is necessary to provide means for the 



36 



MINE DRAINAGE 



escape of air, which will enter the pipe in spite of all pre- 
cautions, and, when once in, will collect at the highest point 
of the siphon because the pressure there is least. Even 
E 




though the joints are perfectly air-tight, the water absorbs 
air, which is given out again as the pressure lessens. Then, 
too, the pipe seldom runs full continuously, and air enters it 
unless both ends are submerged in water. Since the air 




always seeks the highest point of a siphon, sharp bends at 
this point, as at E, Fig. 24, should in all cases be avoided; 
a long bend, or a straight level pipe at the highest part, is 
most satisfactory. 



MINE DRAINAGE 



37 



42. A siphon with a sharp bend, as in Fig. 24, will not 
work well, as the air seeks the highest point E, and is com- 
pressed to an amount represented by the difference in 
pressures of a column of water whose height is s, in feet, and 
one 34 feet (the height of a column of water that the atmos- 
phere will support). Suppose that, in the figure, s = 22 feet; 
then the pressure of the air at E will be 34 — 22 = 12 feet of 
water = 12 X .434 = 5.208 pounds per square inch. This 
pressure will not be materially increased by the addition of 
a little more air. When the volume becomes sufficient to 
occupy the space aEb, the dotted line ab representing a 
horizontal line just touching the bottom of the inside of the 
pipe, the water cannot get through the bend and the siphon 
is useless. This is true also of a siphon with a double bend, 
Fig. 25. Here the air collects at E and F. This is a very 
bad construction and should in all cases be avoided. 

43. A device that will remedy the bad action of a siphon 
to a considerable extent, by permitting the air to escape, is 




shown in Fig. 26. A is an air-tight vessel connected with 
the siphon by pipes B and C provided with valves D and E. 
The pipe B extends to very nearly the top of A, while the 
pipe C just enters the bottom. On the top of the vessel, 
there is a funnel G and a valve F. When the air has collected 
in the siphon and stopped the flow, the valves D and E are 
closed and the valve F opened. Water is then poured into A 



38 MINE DRAINAGE 

until it is filled and overflows the funnel G. The valve F 
is then closed and valves D and E opened. Water will flow 
through C and the air will ascend through B, until the air is 
all out of the pipe. This being done, D and E are shut and F 
opened. The vessel A is then filled with water, F is shut, 
and D and E are opened and left open. Any air that enters the 
siphon will, instead of collecting at JF, seek the highest point 
by ascending through B, forcing a certain amount of water 
through C into H. This will continue until A is filled with 
air, when the valves D and E should be shut and the vessel A 
refilled, as before described. This arrangement may also be 
used to fill the siphon for the purpose of setting it to work. 

44. Discharge of a Siphon. — Theoretically it makes no 
difference whether the discharge end of a siphon is submerged 
or not, but practically it does, for the reason that, if the siphon 
is not flowing full, the air will enter and work its way to 
the highest point. It is rather an advantage to have the 
suction end of the siphon larger than the long leg, since 
the resistance encountered by the water on entering is 
thereby lessened. A siphon will work better when using 
cold water than when using warm water, since water vapor 
collects and opposes the action of the atmosphere; hence, it 
works better in the winter than in the summer. 

The amount of water that a siphon will discharge is cal- 
culated by the formulas given in Hydromechanics for the 
discharge of a pipe. The formulas for the flow of water 
through a rough pipe are taken as conforming more, nearly 
to the ordinary mining conditions than would those for 
smooth pipes. These formulas assume that the pipe is 
running full of water and without any air in it. These con- 
ditions seldom hold in a mine siphon, so that the theoretical 
flow of water is not often obtained. The head is, in all 
cases, the distance marked h in Figs. 22 to 25, and the 
length is the whole length of the siphon from the suction 
end to the discharge end. In finding the head h, it is 
assumed that the discharge end is submerged; then the head 
is the vertical distance, in feet, between the level of the water 



MINE DRAINAGE 39 

at suction and the level of the water at discharge. If the 
discharge end is not submerged, the head will be the vertical 
distance between the level of the water at the suction and 
the end of the discharge pipe. It makes no difference, in 
measuring the head, how far below the water the ends of 
the siphon may extend; the two ends of the siphon may, 
in fact, be level. The head is measured as described and 
the direction of the flow will always be from the higher to 
the lower water level. 

Example. — A siphon has a total length of 1,420 feet of smooth 
pipe, its diameter is 4 inches, and the distance between the water 
levels is 38 feet; what is the discharge, in gallons per hour? 

Solution. — The formulas for the flow of water through pipes as 
given in Hydromechanics may be used for calculating the flow through 
a siphon; the approximate formulas given for rough pipes will be 
sufficiently accurate for most calculations in mining practice, but where 
greater accuracy is required the fundamental formulas may be used. 
The formula for the flow of water through a rough pipe is 

Q = .89 VD 6 "^ 
in which Q = cubic feet of water discharged per second; 
D = diameter of pipe, in feet; 
h = fall per thousand feet of length. 
Substituting the values given in the example, 

n l ri n5 1 . 1,000// 1,000X38 
D = S iL ' n = 243 ; * = —L- = -1A20- 
then 



Q = .89 \/5^-^-^ = .29535 cu. ft. per sec; .29535 X 60 X 60 X 7.48 
\243 X 1,420 . 

= 7,953 gal. per hr. Ans. 

WATER HOISTING 

45. Bucket Drainage. — It is customary, when sinking 
shafts or working mines in which there is little water, to hoist 
it in the regular rock or ore buckets. When a somewhat 
larger quantity is encountered, but still not enough to warrant 
the installation of an expensive pumping plant, a sump large 
enough to hold all the water that will accumulate in 24 hours 
is excavated at the bottom of the shaft and the water hoisted 
in special buckets, similar to that shown in Fig. 27. Buckets, 
or rather tanks, are often used in cases of emergency to assist 



40 MINE DRAINAGE 

the regular pumping plant in keeping water out of mines in 
wet times, when the inflow is so great as to threaten to flood 
the mine and drown the pumps; they have also proved effi- 
cient in unwatering mines that have been flooded and in which 
the pumps have been covered with water. 

Various plans are adopted to use water tanks instead of 
pumps; for instance, tanks may be attached beneath the 
hoisting cages, or water buckets may be hoisted on the cages 
alternately with the coal or ore. All plans, however, that 
require water to be hoisted in the same shaft compartment 
as the mineral have proved objectionable. 

46. Objections to Bucket Drainage. — Where buckets 
are used in shafts, larger sumps are required than are needed 
for pumps, particularly if water hoisting must be carried on 
at periods that will not interfere with active mining and 
hoisting, such as between shifts and at night. Another 
objection to using the main shaft as the water shaft is the 
alternate drying and wetting of the timbers, which will cause 
them to decay more rapidly than if kept dry or wet. Again, 
in cold weather, ice is likely to accumulate in downcast shafts, 
and if men enter and leave the mine under such conditions 
they will be subjected to dangers that should be avoided. 
The filling of the buckets and their discharge at the surface 
are sources of annoyance where the shaft must be used for 
other purposes, unless special arrangements are made, and 
these, possibly, will interfere with others of more importance. 
The objectionable features, however, apply only when a shaft 
must be used for other purposes than hoisting water. When- 
ever a shaft is sunk purposely for hoisting water, the first 
cost is objectionable, but the advantages to be derived from 
the shaft must be considered in connection with the cost. 

47. Advantages of Bucket Drainage. — Aside from 
the cost of the equipment, the simplicity of construction 
and the location of all the operating machinery at the sur- 
face, where it may be inspected and repaired in daylight, 
are of great advantage in hoisting water from mines. The 
machinery, also, is less complicated and requires fewer 



MINE DRAINAGE 



41 



repairs than pumps, besides being less troublesome to install. 
Another advantage is the avoidance of underground steam 
lines with their large condensation losses, besides the 
attendant evils, such as heating the mine air, thus causing 
mine timbers to dry rot and men to suffer when at work, both 
from heat and from the interference with the ventilation. 
Damage to roof and the danger from fire incident to the use 
of steam pipes is avoided, while the troublesome problem of 
exhaust steam does not exist. Pumps must be housed in 
excavations that are strengthened in the best manner, regard- 
less of expense, in order that roof falls and squeezes may 
not occur and injure them. All this expensive work is 
unnecessary when buckets are used for mine drainage. Steam 
pumps, when submerged, will not work to advantage, if at all, 
while a plant using bucket drainage can never be submerged. 



WATER BUCKETS AND TANKS 

48. Water-Bucket Valves. — The water-hoisting bucket 
shown in Fig. 27 is designed for use 
in mines where only a small quantity 
of water accumulates. The valve a 
is raised by the bucket striking the 
water, but is prevented from raising 
too high by the stop b. As the bucket 
is hoisted, the valve seats and holds 
the water until the bucket is dis- 
charged. If there is no valve in the 
bottom, one lip of the bucket must be 
weighted so that it will dip. This 
method of filling buckets is object- 
ionable, since they must turn over on 
the side and allow the bail and slack 
rope to assist in dipping them; then 
when they are hoisted the slack comes 
up with a jerk on the bucket and FlG - 27 

causes it to rock and spill in its flight up the shaft. When 
dip buckets reach the surface, they must be tilted in order to 




42 



MINE DRAINAGE 



discharge the water; valve buckets can be landed in troughs, 
the landing- pushing up the valve stem c and with it the 
attached valves, thus permitting the water to flow out through 
the bottom. 

49. Automatic Bucket Dumps. — One objection to 
tilting buckets is the slopping that occurs when they dis- 




charge their water; suitable arrangements, however, can be 
provided to overcome this feature. Fig. 28 (a) is a plan 
and Fig. 28 {b) an elevation of an apparatus that can be 
used for dumping water buckets. As the bucket a reaches 
the surface, it enters an iron basket frame b that is attached 
to two movable arms c connected to gear-wheels and an axle d 
by the rack bars e. The frame holds the bucket in a vertical 
position until it reaches a point over the trough^ where there 



MINE DRAINAGE 



43 



is no danger of its contents going down the shaft. The 
gear-wheels working in the two inclined top, or rack, bars <?, 
are fitted with teeth, or racks, so that they will move toward 
the hoisting drum / in order to spill the bucket into the 
trough g when coming up. 
After the bucket reaches the 
pivoted arms c, a continuation 
of winding raises these arms 
and in so doing causes the top 
bars e to move from over the 
shaft toward the drum. When 
the tilting bars have assumed 
. the position shown, the contents 
^of the bucket will have been dis- 
charged. The rope now being 
slackened on the drum, the top 
bars will move toward the shaft 
by gravity and in so doing move 
the gear-wheels and the tilting 
bars back to the position indi- 
cated by the dotted lines, from 
which position the bucket de- 
scends into the shaft. The basket 
b not only prevents the bucket 
tilting when over the shaft, but 
also prevents the edge of the 
bucket striking the trough. 

50. Water Tanks. — Water 
buckets not exceeding 200 gal- 
lons in capacity and similar to 
those described are kept in stock 
by mine-supply houses; larger 
sizes, however, are considered 
FlG - 29 tanks and must be constructed 

to order, for which reason a more detailed description is 
given. Mine water is often so corrosive that it is difficult to 
keep rectangular-shaped water tanks from leaking, even when 




44 MINE DRAINAGE 

braced by angle iron at the corners, for which reason cylindri- 
cal tanks are frequently used. 

Fig. 29 shows an emergency tank used at the William Penn 
colliery in the anthracite regions of Pennsylvania. It is an 
automatic, bottom-filling and bottom-dumping tank having a 
capacity of 1,320 gallons. The shell is made of f-inch boiler 
plate and is double-riveted. Four bales a of V X 3" angle 
iron are placed equidistant around the upper circumference 
of the shell, to which they are riveted. The two guides b, 
one on each side of the tank, slide over the shaft guides and 
steady the tank during hoisting. The intake is a flap valve c 
hinged at d and connected, by a reach rod e, with a trip 
lever / that automatically opens the valve by contact with a 
projection in the head-frame. The bottom of the tank is 
provided with a Y-shaped discharge casting, which strikes 
the water in the sump with less shock than it would if the 
bottom were flat. This wedge-shaped bottom, during the dis- 
charging period, also directs the water one side to a trough. 
The objections to this style of tank are: its unsteadiness 
when hoisting at a high speed; its slow discharge; and the 
side pressure created by the water entering the tank from 
one side only. The leverage produced by this lateral pres- 
sure when the tank strikes the water is so great that it 
damages the guides and requires their frequent renewal. 
The large valve is subjected to considerable shock from the 
rush of water, and, even though protected, is subject to 
damage. Flap valves of this description are not considered 
as satisfactory as double valves in water tanks of such large 
size where subjected to heavy blows. 

51. End-Dump Tanks. — The tank shown in Fig. 29 
has given place to that shown in Fig. 30 (a) and (£), which 
is an end-dump tank, 4 feet in diameter inside, made of 
f-inch boiler plate, and double-riveted. The length over all 
is 16 feet 6 inches, and its capacity is 1,440 gallons of water. 
To keep the tank steady in a vertical position, the shaft is 
provided with guides on three sides and the tank is provided 
with a shoe for each guide. The extra, or third, guide and 



46 



MINE DRAINAGE 



its corresponding shoe a are on the side toward which the 
tank dumps. This guide comes to an end at a point near 
the top of the shaft so that, when the dumping wheels b 
engage the dumping rails, the tank, which is pivoted near 
the bottom on the axle c, may swing and empty itself. The 
two valves d in this style of tank are termed butterfly 
valves from the angular positions they occupy when seated 
or opened. The lateral strain on the guides is not so great 
with a butterfly valve as with a single valve, but a further 
improvement is shown in Fig. 31 (a) and (b), where an open 




casting having a central partition forms a perfect wedge, 
thus entirely avoiding the side thrust that would come on a 
slanting discharge bottom. It will be observed that the 
valves a, Fig. 31, swing outwards, instead of inwards, and 
seat in the center. 

52. Hoisting Water on Slopes. — Water tanks are also 
sometimes used both in emergencies and permanently for 
unwatering slope mines. These tanks or cars are arranged 
to dump into water-tight chutes, and taken as a whole the 
system would be quite effective were it not for the objection- 
able features that are mentioned in the following articles. 



MINE DRAINAGE 47 

53. Water-Tank Car Wheels. — Slope car wheels run- 
ning in the same straight line soon become grooved, even 
tinder the most favorable circumstances; but when the car 
wheels are dipped in acid mine water, the wear is materially 
increased. The water dripping from the car also corrodes 
the rails; and if that water is very acid the rails in the 
sump are quickly destroyed. Unless special arrangements 
are made, the journals and journal boxes soon become 
corroded, necessitating repairs. These objections have been 
overcome, to a certain extent, by making the flanges on the 
wheels high, to keep them on the track, and by using self- 
oiling wheels with bronze bushings that fit closely over 
bronze collars on the axles, instead of ordinary car wheels 
and iron axles. These arrangements are effective so far as 
the corrosion of the journals is concerned, but the grooving 
of the wheels, and the expense of replacing wheels and soft 
bronze bearings, have not been overcome, particularly on 
slopes with slight inclination. 

54. Speed of Hoisting Water on Slopes. — Owing to 

irregularities that occur in slope tracks and to other condi- 
tions, which may cause the slope car to leave the track, the 
speed of hoisting is always less on slopes than in shafts. If 
the car strikes the water at a high speed it will in all 
probability leave the track, while if it enters the water at 
only moderately high speed, a small chip on the track or 
some submerged object may cause it to be derailed. 

55. Operation of Tanks. — To successfully operate 
tilting water tanks, a rest must be arranged in the sump on 
which the lower tank, which is filling, is supported while the 
upper tank is discharging. Should the filling tank sink too 
deep in the sump, it would turn the tank at the top upside 
down and possibly damage the sheave. Discharging the 
water causes a sudden reduction in the load, which makes 
the operation of discharging somewhat delicate in deep 
shafts. Unless the hoisting brake holds the drum firmly 
when a tank is emptied, the sudden release of weight may 
allow the weight of the rope in the other compartment to 



48 



MINE DRAINAGE 




MINE DRAINAGE 49 

move the drum enough to turn the tank upside down. These 
difficulties have been overcome in great part by the arrange- 
ment shown in Fig. 32, which was installed by the Union 
Coal Company at Shamokin, Pennsylvania. Fig. 32 shows 
the surface arrangements at this plant and the guides for 
keeping the car on the track as it enters the sump. The 
large iron tank car a, holding 1,400 gallons of water, is pro- 
vided with a bail b that is pivoted on the axle c, which 
extends from side to side through the car and engages with 
plate guides d in the head-frame. The tank is also fitted on 
the sides and top with guide shoes e to engage the guides / 
at the bottom of the slope. The guides / extend 20 feet 
above the maximum water-line and hold the car on the track 
when it strikes the water. There is then no danger of 
floating substances derailing the car at the surface of the 
water; and since the slope has 70° pitch, there is no danger 
of submerged obstructions remaining on the track. The 
guides are thoroughly braced sb as to take up any strains 
that may be put on them when the car strikes the water. 
This is a double hoist, one car ascending while the other is 
descending; consequently, to prevent the upper car being 
raised too high at the landing, a timber rest is provided in 
the sump for the lower car. 

56. The Gilberton Water Shaft. — Water hoisting, in 
cases of emergency, is quite generally practiced, but as a sub- 
stitute for pumping, the system has probably been most fully 
developed in the anthracite mines of Pennsylvania. One of 
the most extensive drainage shafts is the Gilberton water 
shaft, which is 1,070 feet deep and is intended to drain two 
collieries connected by a cross-cut tunnel. It is used exclu- 
sively for water hoisting, lowering supplies, and taking 
miners into, and out of, the mine. There are four shaft 
compartments; two 7 feet square for the water tanks exclu- 
sively, and two 11 feet 3 inches long by 7 feet wide for the 
men and supplies; the Tatter compartments, however, may be 
quickly changed for hoisting water. The shaft outside, is 
*26 feet 8 inches by 22 feet; inside, it is 19 feet 6 inches by 



50 



MINE DRAINAGE 




14 feet 10 inches. The 
maximum drainage was 
calculated as 6,000,000 
gallons daily during the 
wet season; and as most 
of this water would find 
its way into the lower 
levels when they are 
opened, it would require 
a very large pumping 
plant to handle the 
water. The question of 
building pumps and 
establishing central sta- 
tions, to which all the 
water could be directed 
was thoroughly con- 
sidered and weighed 
against the advantages 
that would be derived 
from sinking this shaft. 
The machinery neces- 
sary to hoist water from 
this shaft is two pair of 
direct-acting horizontal 
engines, set as shown in 
Fig. 33, each with two 
steam cylinders 45 
inches in diameter and 
60 inches stroke. The 
hoisting drums are 14 
feet 8 inches in diameter 
by 15 feet long, on each 
of which are two cruci- 
ble-steel wire ropes 2 
inches in diameter and 
1,300 feet long. At fifty 
revolutions, or 500 feet 



MINE DRAINAGE 51 

per minute, piston speed, the drum will hoist at the rate of 
2,300 feet per minute. The drum makes 23.87 revolutions 
for each trip, hoisting from a depth of 1,100 feet. The ropes 
fasten in the center of the drum and wind toward the end, the 
fleet of the rope being 50.72 inches. 

The water tanks for hoisting are of iron, 5 feet 6 inches in 
diameter and 14 feet long, making their capacity 2,400 gal- 
lons each. They are fastened to the rope by four chains of 
li-inch iron, the chains being fastened equidistant on the 
circumference of the tanks. The valves in the bottom of the 
tank are arranged to open and close automatically, similar to 
that shown in Fig. 29, being opened by the guide shoes 
striking trips attached to the head-frame. The bottom of 
the tank has a side discharge similar to that described. 

With the engines running at normal speed, two tanks of 
2,400 gallons each should be hoisted per minute; this gives 
120 tanks per hour or 2,800 tanks in 24 hours, amounting to 
7,000,000 gallons per day, which is in excess of the estimated 
quantity by 1,000,000 gallons. By a slight increase in speed, 
700,000 additional gallons of water could be raised daily, 
which, it is considered, will cover all emergencies; but if it 
should not, the other compartments can be depended on 
to supply the deficiency. 

COST OF WATER-HOISTING PLANTS 

57. The following costs of constructing and operating 
water-hoisting plants are given by Mr. R. V. Norris in a paper 
read before the American Institute of Mining Engineers. 
The cost of constructing two water hoists, including the cost 
of shaft sinking, head-frames, steam lines, and boiler plant 
at the Lytle and William Penn shafts of the Pennsylvania 
Railroad were as given in Table I. The cost of the shafts 
vary, one being more difficult to put down than the other. 
The steam lines are some distance away from the boilers in 
both cases, which accounts for their high cost. 

The cost of operating the two water hoists given in Table I 
and another similar hoist operated by the same company is 
given in Tables II and III. 



TABLE I 





William Penn 
Water Hoist 


Lytle Water Hoist 


Depth of shaft 


953 ft. 


1,500 ft. 


Capacity of tanks .... 


1,440 gal. 


2,600 gal. 


Size of engines 


32 in. X 48 in. 


36 in. X 60 in. 


Size of drums 


Straight 12 ft. diam. 


Cone 10 to 16 ft. diam. 


Capacity of hoist, 24 hours 


2,100,000 gal. 


3,750,000 gal. 


Best record, 24 hours . . 


2,291,040 gal. 


3,772,600 gal. 


Cost of sinking and tim- 






bering 


$20,673.81 


$22,641.63 


Cost of head-frame . . . 


4,224.13 


3.540.58 


Cost of water-hoist en- 






gines, foundations, and 






house 


15,583-64 


29,653-17 


Cost of tanks and ropes . 


2,393.23 


3,899-65 


Cost of steam line .... 


3,726.12 


4,95i.i7 


Cost of boiler plant . . . 




16,091.76 


Total cost 


$46,600.93 


$80,777.96 


Cost, excluding shaft sink- 






ing and steam plant . . 


$22,201.00 


$37,093.40 


Cost per 1 ,000 gallons daily 






capacity, excludingshaft 






and steam plant .... 


10.57 


9.87 



TABLE II 





Plant 




Luke Fidler 


Wm. Penn 


Lytle 




Length of Time in Operation 




3 Years 


37 Days 


1 Month 


Depth of shaft, feet 

Quantity hoisted, gallons .... 
Average height hoisted, feet . . 
Cost of labor, repairs, and sup- 
plies per 1,000 gallons .... 
Cost of steam per 1,000 gallons . 


960 

918,501,200 

960 

$.0114 
.0192 


953 

112,468,080 

727.8 

$.0088 
.0146 


1,500 

236,906,000 
740.6 

$.0071 
.0148 


Total cost 


$.0306 


$.0234 


$.0219 





MINE DRAINAGE 
TABLE III 



53 







Estimated Cost per 1,000 Gallons, 1,000 
Feet Vertical Hoist 




Luke Fidler 


Wm. Perm 


Lytle 


Labor, supplies, 
hoisting . . . 


and repairs for 


$.012 
.020 


$.009 
.020 


$.008 
.020 








Total . . . 


$.032 


$.029 


$.028 



HOISTING VERSUS PUMPING WATER 

58. The average cost of pumping water at the Lykens 
Valley Coal Company is given by Mr. Norris at 5.33 cents, in 
1901, and 3.9 cents, in 1902, per 1,000 gallons. The cost of 
pumping at the Lehigh Valley Coal Company's Hazleton shaft 
is said to be 1.25 cents per 1,000 gallons for 560 feet vertical 
lift; this is considered one of the highest-grade mine-pumping 
plants in Pennsylvania. In comparing the cost of water 
hoisting with the pumps at the Lykens Valley Coal Com- 
pany, it will be noticed that there is considerable saving in 
favor of water hoisting; on the other hand, when comparing 
the cost of pumping at the Hazleton shaft with water hoisting, 
it will be found that the pump shows a considerable saving. 
This may be partly accounted for by the difference in shaft 
depths, the Hazleton shaft being 560 feet deep, while at the 
Lytle shaft water was hoisted 740.6 feet. This is not 
sufficient to account for the difference of .94 cent, in favor 
of pumping, and in comparison it should be considered that 
the steam cost of hoisting could also be reduced by the use 
of compound engines. When shafts are more than 500 feet 
deep, the advocates of water hoisting claim that it will proba- 
bly be found more economical to use water hoists than steam 
pumps. Their claim is, however, not admitted by the advo- 
cates of pumping under similar circumstances. 



